I may be biased, but May is the best month for walking in Scotland. Spring is well under way so the winter weather is over, hours of daylight are good, snow will be gone apart from the hill tops, and the first midges will not have hatched.
Be aware that we don't have the manicured trails that you get in many places, paths are rougher and not sign-posted. You may need to read a map. Avoid the WHW unless you enjoy the sounds from a road (highway).