I've never heard of reproducing melons vegetatively. You can always try it and let us know how things turn out.
Personally, I prefer not to use vegetative reproduction as the offspring are just clones of the parent plant with no genetic or phenetic variability. However, if you use seeds; each plant will be slightly different from the parent plant and have the possibility of being resistant to disease, cold tolerant, heat tolerant, have better flavour(the melons) and so on.
Use the Q-tip to cross pollinate plants once the flowers appear. I think that melons have individual sexes so, you'll have to take the pollen from a male flower (plant) and cross that with the female flower.
Pollen is found on the Anthers (the male structure of the plant) and you need to dab this on the Style (the femaile structure of the plant).
Ask Franco about the sexes of melon plants, he did some research on it last summer.
(You can actually buy black q-tips that make pollinating a bit easier because you can see the pollen that much better. Try a local science shop like McGill and Orme or ...... I'm forgetting the other place that I go to.