And would you want your feet to have prolonged contact with the residue of some form of pedal Radweld?
In theory it is possible. An organic solvent such as acetone or ether will dissolve a plastic such as polystyrene and is volatile enough to leave a residue of plastic when it evaporates. The main problem is you would need a plastic that remains flexible when it deposits, polystyrene may become a bit brittle as it comes out of solution. I suppose a couple of tubes of seam stopper in acetone might work, not sure if it is cleared for skin contact though. Bear in mind that the residue will be all over the inside of your boot up to the fill level.
Of course, if you used ether you would be as high as kite in no time as it is an anaesthetic, acetone is nail varnish remover and, like ether, is fiendishly flammable. I would avoid petrol as a solvent, I'm not sure if it has benzene in it but if it does that is a known carcinogen. Acetone is volatile enough to evaporate completely from the boot provided the boot is well ventilated - you might need an air line to get rid of it.
If you do try it, best buy that charcoal filter mask first though and work outdoors just to be safe. Final thought, if your boots have a membrane lining, I am not sure they still would have after exposure to a powerful organic solvent - might be fun finding out though.