The seals have the potential to bite through your hand- so my advice is offer a fist at first until you are very aware of exactly what's going on.
They will only be mouthing your hand to check what you are made of and at times (mainly pups) the whole thing can turn into a great game .... not dissimilar to a dog playing with a stick whilst you have hold of the other end!
When this happens you have to be VERY careful as there is a fine line between boisterous behaviour and a chew that is a bit too hard and could easily break your skin!
Seals have a number of bugs in their mouths (including Strep grypus (a new species 2005!) and some mycoplasma) these have the potential to cause unpleasant infections.
Dog bites aren't as bad as cat bites which aren't as bad as human bites (in terms of infection risk).... I'm not sure where seals fit into the order!
I once forget my gloves (idiot!) I don't wear them just to keep warm, I wear them to provide some slight protection from chewing / mouthing.
I ended up playing with a very boisterous seal pup who thought that it was a great game to bite my hand and attempt to pull my wife's hood off!
Eventually she calmed down a little but she did nick my hand with her needle sharp teeth. I bled it underwater in the salty water and it never got infected.
For more guillemot clips ...that are better have a look at
YouTube - Broadcast Yourself.
Safe diving,
Ben "Seal diver"