There have been a large number of discussions on this and other sites, discussing the same or similar questions. The technical answer seems to be "maybe". The real answer seems to be dependent on your own risk-comfort level. If you believe that the weight of the engine is the determinative factor, then a 9.9 four stroke is probably close to the weight of a 15 hp two stroke, and you should be ok. However, if you are concerned that the torque generated by a 9.9 hp four stroke is higher than that of a 15 hp two stroke, then the engine bracket is probably not strong enough and should be replaced. I've seen both argued here and elsewhere.
My two cents (adjusted for inflation): if the engine bracket is old, then its probably worth replacing with one that is specifically rated to handle your engine.
Remember, advice from essentially anonymous people on the internet is worth exactly what you pay for it. This is your boat, and you are responsible for it, yourself and your passengers. Do your research, talk to (live) experts and go with your gut.