Clawfoot Tub Trap

adding a p trap to upstairs claw foot tub hello all, new member here, I am  in the middle of remodeling an upstairs bathroom in a 1908 home.  1. is there was no vent stack originally, do I need to add one (I am in the county and doesn't have to be inspected or permitted).  My wife doesn't want to since it would require destroying old wallpaper to open up a wall to run the stack up to the roof, she says it worked without one before so why add one now.  2. the clawfoot tub had some sort of led box trap under the floor and I want to add a p trap to the new plumbing.  All photos of claw foot tubs show the drain without a p trap, which is fine on a single story home since it can be under the house, but is it safe to put a p trap enclosed between the floor and ceiling on the 2nd floor?  Doesn't seem enough clearance to put it above the floor...whats the answer.  Any suggestions or help would be greatly appreciated. correction....should read "lead" box trap, not led box trap
Under the floor is where I have always seen the bathtub trap.  It is a devil to install a new one unless you have access from the ceiling below.  As far as the vent goes when they plumbed my kitchen I didn't want pipes going up through the whole house either.  They installed a cheater vent right beside the sink.  It is a pvc fitting with a a rubber flap and a spring in it.  It allows air to enter the drain pipe but no sewer gas to come up and out into the room.  They called it a "cheater valve" , ask about it.   While putting insulation in my attic, I noticed some old utilities coming up through the floor.  This is where I ended running the vent pipe for my bathroom and I didn't have to tear up a wall to put it in.  You might check in your attic to see if there is a wall cavity like this in your house (some old houses have many of them).  If you use the cheater vent, put it in a place that you can change it out (they go bad sometimes).  Maybe hide it on the backside of the tub or build a partial wall with a door to get at it.  
Some codes don't allow them, but they are still sold at the hardware stores in those areas. Thanxz to Lair and Andy for the responses above, haven't heard of the AAV system before but looked it up on line and it may be the answer.  Edison Light Bulb Was An Energy Converter What Does That MeanOne handicap is that the plumbing lines are on an outside wall which eliminates any space in the attic for doing anything as the rafters rest on that wall cap creating a very small space in the attic on the inside surface area of the wall. Habitat Single Duvet Coverscan't go outside the wall and up as it would be visible from front walkway, can't go inside the wall because wife won't let me mess up the wall paper.Homes For Sale In Copenhaver Potomac Md
I am thinking of a series of those AAV vents (1.5 inch) one hidden under the lavatory inside the cabinet, one on the back of the tub drain (not real visible between the tub and the wall) that would provide 3 inches of vent. P traps don't work worth diddle on tubs and showers, and PVC tub traps are cheap and easy to work with.  Do it right, or wish you did a few years down the line when you're snaking a hair plug that cruised right past the P trap. As to vents, consider that a vent on a sink or tub does not really need to be the full diameter of the drain to work.  Since you don't have to consider inspection a little looking around might well enable you to snake a 3/4 PEX vent up to the attic, and couple all those PEX vents into a single 2" stack through the roof.  It will work very well for venting, and you won't smell sewer gas if the trap goes dry. thanxz Franz, that gives me some ideas. Not sure I understand your comments about the p traps though.  Seems that there must be  a p trap for the tub to prevent sewer gases.
Here is an attempt to explain my configuration: Tub - Lavatory- Toilet all side by side with little room in between/ drain from tub leads to drain from lavatory (all 1.5 inch) which leads to 4 inch toilet pipe.  I figure I can  put a 3 or 4 inch automatic air vent hidden in the cabinet of the lavatory which would suffice for the toilet and lavatory, even possibly for the tub.  The Lav would have a p trap and the toilet a internal one, but now I have no way to block sewer gas from coming down the line and up through the tub.  The end of the tub is almost against the outside wall with the length running almost against in interior wall.  No room between the tub and floor to put a p trap there, which leaves the only option of having one under the floor...which would be problematic for future blockages, etc as you mentioned. I was wondering, could I do away with a p trap on the tub, just make a straight connection to the rest of the drain pipe and use a rubber plug in the bottom of the tub to prevent sewer gas from coming up??  
open time would be minimal, just to drain tub after a bath and then put the plug back in place when the last of the water goes down the tube.  This seems like ti would solve the problem with minimal expense and effort (I do plan on putting in on to the vents described above, coming up under the lav. cabinet). Bob, you still should put a trap in of some type to prevent the sewer gases from coming up through the tub drain.  You'll have to ask some one else on the tub trap though, since I haven't ever used one.  I just used a p trap when I did my tub.  It did clog once, but a plunger did the trick.Fit-All Sink Strainer, Stainless Steel Sink Strainer, Satin Nickel Brass Bath Waste Kit Twist and Close 1-1/2 in. White Poly Pipe Bath Drain in Chrome Easy Touch 1-1/2 in. Plastic Bath Drain KitPVC Square-Head Shower Pan Drain in Chrome Tub and Shower Drain Covers in Oil Rubbed Bronze Clearflo Brass Slotted Overflow Bath Drain in Vibrant Brushed Nickel