I want to know which one of the two branches will dry earlier. The one with leaves or the other that has removed leaves? I want to transfer a bud for grafting from some distance and i want to keep the bud fresh. So is it better to remove the leaves from the scion or keep them? Will the leaves dry the scion earlier?
Standard practice for bud sticks (used for budding/bud-grafting, cut with leaves on) is to cut the leaves but leave the leaf stem as a handle, precisely because the leaf will tend to dry the stick by transpiration.
Scions for grafting are cut when dormant so they don't have any leaves anyway.
Some types of trees graft much better by one means than the other, others can be done either way, at different times of the year.
Both are also commonly transported with damp paper (often in a plastic bag as well) and preferably refrigerated (but not frozen.)
In theory yes is the answer if anything left with a leaf on it will by evapotranspiration should dry out the plant material- but it will stress the plant slightly- the more leaves the more water lost. Again it depends on what your doing with what plant- some plants will weep more, some will just bleed and bleed depending on how sappy the growth is- I think you'll want a mature-ish material for the root stock and a "as fresh as possible bud"- I would take a large amount of material with you, so giving yourself as many buds for grafting as possible(keeping them well hydrated in a plastic bag during the journey)and with some luck and practice, plus "a lot of goes" you should have some success- it will also need you to do some home work on time of year this should be done- as the plant material will need time to heal- and also have a look at a sharp knife and techniques available to use- the most obvious isn't always the best way. And most importantly keep everything really clean! an infection can ruin everything! hope it helps and good luck.