I would spring for the $12 for a sponge filter and a few bucks for a cheap air pump. My other suggestion would be a small cheap heater just to keep the temperature in check. Might be $30 all together.
Good thing is though, when the fry are big enough to put back into the main tank you should have a good little quarantine tank ready to go with that 10g tank
Platies are pretty hardy but I would be worried about the temp and high ammonia content of not having a filter or heater. The bio-load on fry should not be huge, and teh combination of sponge filter and air/water movement should help dispel some ammonia.
When you move the fry back to the main tank also move the sponge filter back to your main tank. That way it will be ready to go for the next time.