Don't much care for the acid-oozing shortswords, it's a stretch to far from the ur-text, which gives no reason to think they're not regular metal blades. I'd assumed they keep the ooze's acid inside their skin, which is why it doesn't corrode their grafted shortswords, but when an attacker causes them to bleed it corrodes the weapon.
EDIT: Upon reflection, I prefer metal shortswords that are alchemically treated to be immune to gray ooze and grayman acid. :ENDEDIT
That does raise the question as to why the description only refers to the times it takes for their blood to corrode armour. Do they spray out blood upon an attacker? I think it's just a carry-over from AD&D, 3E SRD gray ooze's can dissolve weapons immediately, but there's no mention of them affecting armour.
So, I'm in favour of the greymen doing ongoing acid damage to any metal weapon that injures them and leave it at that. You'll notice that their acid only dissolves metal, not organic items. The grayman may alter the trapped gray ooze's acids somehow so it does not dissolve its body. Maybe this effect ends when the grayman is destroyed, and the ooze eats its way out ot the construct's body?
I do agree with immunity to acid, though possibly only until the grayman is "killed".
I'd vote against intelligence for the gray ooze. Just make it a regular gray ooze, and assume the Int 1 is intrinsic to the grayman.
Oh, and since it says their acid works half as fast as a gray ooze, I'd halve the acid damage to 8 points per round instead of the 11 points in the current version of our conversion.