Obviously I can not advise whether or not you should do physio, delay starting etc
As an outpatient specialist I would say that at times your hands do work hard...this does depend often on the type of patient you are seeing. As a student in my first year I was having problems with hypermobile thumbs and saw a specialist who advised me to avoid outpatients as a career choice...this went down like a lead balloon with me, I ingnored him and carried on. I have tried splints...find them difficult to get on with. There is a book for physios on how to protect your hands (can't remember the title) it may help. I have personnally found that if you are careful and watch that you don't over do it then you can manage a lot of these things. Depend though on your individual problem.
If you haven't already try and get some work experience (if you can...I know it is hard to get into) in the NHS so that you can assess a variety of areas of physio and try and gauge whether or not you think that your wrist is up to it.
Good luck