It depends how many volts the peltier requires, it it needs 12v to function then yes, the 12v wall wart will work.
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Without knowing the current draw, you can't assume that any given wall wart will work.
Best source of warts adequate to task is those made for ITX computers and such, capable of 12V at around 8A and sometimes more. They have a small fan in so at that much power they'll likely whine a lot.
One thing with TEC's (Peltiers) is they're often made for standard voltage anyway, so when you but a 12V one at some overclocking shop you'll actually be buying one that has a top voltage of 15.4V or similar. They are NOT efficient at top voltage(called Vmax), so trying for the maximum cooling pump power (called Qmax) isn't worth doing. This is just background info anyway, while you can get them from Melcor and Marlow (and I strongly suggest getting their downloadable info, it's good general reading on the subject), you're usually better off buying from overclockers because they pass on the bulk savings. Even used ones on eBay aren't too shabby, specially if you want several at once. Which is wise because if you want lots of cooling, do it with several run modestly instead of one run hard.
Like Plasmana said, wall wart should give voltage required by peltier. Another thing, is current: if your peltier is 96W at 12V, you need 12V wall wart that can supply 8 Amps (96W / 12V = 8A)