I suggest you ask around your dojo for suggestions. I know someone up here in Canada, but that would probably be too much trouble for you.
Rewrapping is something you can learn for yourself if you like, but it will take you many months of practice to get a nice, solid wrap. I wouldn't recommend trying to learn to save money.
A rewrap shouldn't be very expensive. About $100 total maybe? Of course the better the work the more expensive it will be. Fred Lohman charges $200 for a handle rewrap I believe.
If nothing else there is Thomas Buck at www.tsukamaki.net
, and he's not so far away (Minnesota I believe). You would send the handle to him and then get it back in a month or two. Of course this supposes you can take your sword apart and put it back together again, which may not be so simple if it is shimmed and everything.
You should ask your sensei, I am sure he could give you good advice for this.