I've done this a number of times now - you should be good.
for what it's worth, what i have done is to create the new .kyr & .sth files with a slightly different name, so i can copy them out to the server data directory and not overwrite the current certificate files.
Then i update the certificate name on the internet sites doc, and a few minutes later issue a 'tell http refresh' at the console. The new certificates should be picked up.
Then, if there are any issues I can revert the names back on the internet sites doc.
Another option of course is to just replace the current .kyr & .sth files with files of the same name. I'd rename the old files first, so that you can rename them back if troubles occur.
Having said all that, i don't think I've ever had any trouble with the new certificates.