Very experienced Argyle Clarke...

[megamole]

... is basically unkillable if you don't have slaying ammo or can't spam ball spells.

Fights in darkness, spams disarm, picks up your weapon, regenerates about 25 hp a round, heals to full if he's not one-shotted.

Any advice?

[Grond]

First off, you could just not deal with him. You probably don't get anything substantial out of it.

If you must kill him, the darkness is probably to your advantage. Master swordsman doesn't see in the dark, so he's less likely to disarm you there, and you have the chance to get backstabs. If you've got any +Dx items or boost dexterity potions, you might want to use them, as it will make disarming less likely to work (full immunity to master swordsman disarm comes at 29 Dexterity).

You can try to stack up poison to counteract the healing, either by periodically dipping your weapons in poison or zapping wand of poison. If you've got shock resistance or immunity and a wand of lightning, you could try killing him with bounced lightning bolts. This should be very effective as master swordsman has no chance to shrug off the bolts.

As far as instant kills go, luring him to an altar and sacrificing him, luring him to the banshee, and wand of death should all work.

[megamole]

Sadly he's blocking the way down and has taken the scorpion spear and Rolf's Companion off my dwarf. I want those back dammit.

[Grond]

One more idea: you could try polymorphing him. Two cursed potions of raw chaos should be enough to transform him into a writhing mass or chao mutant (if he has a healing spell and you don't have staff of dampening, this might be a terrible idea). He will probably retain his special abilities other than disarming in this form, but will become vulnerable to a potion of cure corruption (which will remove his regeneration). Successful potions of exchange will immediately neutralize him (and drop what he's picked up), but it's possible for him to dodge these.

[Blasphemous]

Supercharged wand of death in a bouncy corridor.

[grobblewobble]

Any advice?

Don't fight fairly. Use your resources. Do you have a wand of paralyzation? That's just as lethal as a wand of death.

Or a supercharged wand of fireballs, for instance? There are many solutions, it all depends on your resources. If you want better advice, post a dump of your character including his interesting items.