If it's one of those electronic (no compressor) ones you can take it apart to get the psu and peltier junction, and then bond the cold side of the peltier onto a forced convection heatink which has the inlet air blown through it. This will precipitate moisture, which has to have a path to drain away. The other side of the peltier will get very hot, so you'll need another ducted heatsink arrangement to draw that heat away and exhaust it elsewhere (or it burns out) .

What is the wattage of the fridge? It probably won't cool a very large volume of air, but based on the wattage and the temperature drop you want, the flow rate can be calculated. Or given the total volume of the box you're cooling, and how well insulated it is, it would be possible to roughly work out whether a given peltier would achieve a given degree of cooling.

Bear in mind the guts of the fridge are only designed to chill a small and very insulated volume.

You might get a few degrees in a moderate sized cabinet, I'd guess.