Hi,
I am guessing your halyards are external and therefore you only have two? If so, you'll find that you have 4 sheaves at the mast head, two per side. This way, each halyard runs up and over a pair of sheaves port and starboard, respectively. You won't be able to replace the sheaves because they'll be in use by the halyards that are holding you. That brings up a second point, going up on only a single halyard when one has already broken is pretty damn risky. What's to say that the one you are using to go up won't break? Really, don't do this. Leave this one to a pro who can safely deal with your scenario. I don't mean to be a downer on your adventure, and I actually enjoy a trip up the mast - it's pretty cool view from the top, but given what you described, you're life is worth paying a few bucks on this one.