The problem from a medical point of view is that you're 29 and have a DVT.
You need to understand that every medical procedure carries risk.
There is a standard assessment, always made, even for aspirin. Does the benefit outweigh the risk? If yes, then the procedure can go ahead.
It's that simple really.
Now, if you have a problem which could put you at greater risk with the procedure, then only a totally callous and unprofessional Dr would do it.
If the reasons why you have the DVT are traceable, and manageable then the procedure can go ahead.