Lightsabers only produce heat incidentally, so your flesh would burn, not cauterise. (Not hot enough....though would set surrounding clothes on fire).
Against Adamantium though, it would deflect off; and require holding it against the Adamantium to cut (not melt) through it.
(You can see similar with Thermite versus Titanium)
Simply: Lightsabers are shaped plasma; if Obi-Wan struck Wolverine with it, it would shear through his flesh, but dissipate around the Admantium.
(Proof: Lightsabers in Star Wars do set damage, Adamantium in Marvel deflects all heat up to pure nuclear fusion (Sun))
Caveat: The flesh around the Adamantium WOULD cauterise as the Adamantiums heat would cauterise the wound.
SteveZim1017 said:
how about we just make a vibrosword out of a carbonfiber/graphite core with an edge of antarctic vibranium (anti-metal) and call it quits.
Problem, Vibrainium absorbs energy (mostly sound), so the blade couldn't vibrate. A mono-molecular Vibranium sword could work, but it'd still have problems being swung too fast.