You don't touch sword blades most of the time you use them either. It is lighter, but nothing a few practice swings couldn't get you used to. I see no reason why at least a little melee or lightsaber skill should transfer between them.
Actually, many sword techniques do use hand on blade, especially those for European 2-handed swords. Then again, most European swords weren't particularly sharp, either - they work by concentration of force, like an axe, rather than by sharp-cutting. Rapiers and Smallswords, however, tended to be sharpened near the tips. Plus, many swords were single or one-and-a-half edged. (The latter having two edges, but one side only half the blade length.)
Plus, many swordsmen are trained to be slapping opposing blades if their shield is absent or disabled; it's quite a viable technique for making your opponent's swing hit something other than you.
And for comparison, most SCA Heavies have a bit of a roguh time transitioning to Rapier - the rapier is about half the weight and half again the length, and the abrupt change makes them clumsy with it for weeks. And those are both melee weapons. (They learn the footwork faster, tho'. And already have the needed awareness of opponent.) It's not an impossible task for them to transition, but it isn't a "just a few swings"...
And the Lightsaber is much further difference.