You need to make sure that replacement shifter/brake lever units are compatible with both the cantilever brakes and your derailleurs.
Tektro does not seem to make the 992 cantis your Jamis has anymore but I found a couple of online stores that claim they are comparable with STI road style levers.
Your Jamis has Shimano Tiagra/Sora derailleurs so you need Shimano shift levers. Matching Tiagra Shift levers would obviously work well.
Switching out levers is relatively straightforward. There are plenty of guides on line that will help you onstal and connect the new levers (The Park Tool Company YouTube channel is my favorite). The difficult part is that you will have to remove the bar tape to get the old levers off and new shift levers on. Replacing bar tape is tricky of you have not done it before.