You should really look into samplers. The problem with the mp3 player is that if you take it and a speed even a little less than you used on the recording, then the sound triggers too late, or too soon. If you have the cash, I would think about a SP-404.
http://www.musiciansfriend.com/produ...-FX?sku=700451
Allows you to also manipulate the signal with reverb, EQ, filters and such.
If that's a little too pricey, Digitech's JamMan is mainly a looper, but can also be used for a sampler. Just get a flashmedia card, load up the samples and assign them numbers. Scroll the knob so the number on the pedal matches up with the sample you want, and hit the pedal.
http://www.musiciansfriend.com/produ...dal?sku=156600
Also, look into a Used JamMan, they go for like 150, and usually they're pretty easy to find.
Edit: Oops, missed the bit about not effecting the timing. That could work, but you also run the risk of file compression and not sounding alright. Plus the adapters would be a minor hassle for connecting.