Is a 4 unit bridge from 9-12 with 12 being a cantilever a good option?

I would suggest a single crown on #9 or a veneer to match esthetics.  An implant is one option but since the patient prefers to avoid an implant I would suggest a single crown on # 11 with a pontic (tooth replacement) in the space of 12.  In order to supply support I wold create a rest preparation on # 13 into the existing bridge abutment.This would give good occlusal support to the pontic.  This is called a stress breaker and it has a long history in dentistry.  It will prevent undo forces being placed on tooth #11 and it will not require the expense of replacing the posterior bridge.  A bridge from 9,10, 11 will be much more difficult to maintain.  An implant is not always the best choice for patients for multiple reasons.  Recent studies have not shown superiority of implants over bridges in well maintained mouths.  I have bridges that have been in patients mouths for over 30 years.  

The best choice would be the dental implant, and reluctance for that should be explored (it likely is the best choice).  If a cantilever is insisted, it should hang off of the bridge from 13-15 and adjusted so that no bite forces are on #12.  Treat #9 seperately.