First of all you should try disassembling and cleaning out the old shifters with WD40. I've never cleaned out a 10sp shifter but I've brought several 7-8 sp brifters back to life.
Secondly, you can get Microshift shifters which will be fully compatible with your Shimano shifters, without having to fuss with Shiftmate, etc.
Third option would be the Tiagra 4600 brifters (ie. not 4700). They are still available new on Ebay.