I would have the remaining bit of claw removed Colin just in case dirt gets in there, a salt bath 4 times a day helps and I use Gentian Violet solution, you can also use Hydrogen Peroxide (10%) solution, this helps the quick to withdraw and helps protect it.
Just keep it clean and don't cover it with a dressing, let the air get to it.
Nero lost a claw this spring when he scraped the ground after having a wee, dogs do this to leave their trade mark so to speak, it took a while to grow back in again but he's OK now.