I would do a 50% or more change per week. Small tanks get waste built up pretty fast. I do 50% weekly changes on all my tanks, though, except my betta tank which is a little smaller than yours, I change all the water in there a few times a week. Keep an eye on the nitrate and change water accordingly. You want it under 20, and a 50% change will reduce the nitrate level by half, and so on. With such a small water volume, large changes are easier, so I almost always change almost all of the water in small tanks each week because it is simple to do.
If your room temperature is stable, you should be able to do without a heater for a while, but it would still be a good idea to pick up a small heater just to keep the temperature from fluctuating too much. Also, Cories should not be kept in such a small tank, they do best with a small school and really need a 20 gallon tank or larger. As long as you are vigilant about the water changes, the small tank should be ok for treating the swordtail. Keep an eye on the ammonia levels in there, though, and change the water at least once a day. Melafix will do no good in water filled with the same toxins that lead to fin rot and worse. Remember, ammonia is toxic even at low levels and it will kill your fish if it is allowed to accumulate. There is no filter and nothing for beneficial bacteria to grow on, so ammonia will not be converted into nitrite and nitrate!