I am not sure how to answer this...other than there are no guarantees with anything.
Neutering an older dog....in my opinion doesn't change him that much. It takes several months for testosterone levels to drop...
The marking everything will sometimes decrease...territory issues may decrease slightly...and even a slow down of metabolism so watching his weight. I don't feel his 'personality' will change.
Any surgery will be harder on an older animal, but presurgical bloodwork, good IV support during surgery, and monitoring...should yield a low risk. The surgery itself is quick and doesn't involve going in the abdomen...so surgical difficulty is minimal as well.
Prostatic hyperplasia is pretty uncomfortable...so I do feel you need to do something, because chronic pain can cause personality changes as well.
If you castrate a dog with BPH, the prostate should decrease 50% in size by 3 weeks, and by 70% by 9 weeks, and may be completely involuted after 12 weeks.
Do you have to neuter? No. There are medications to chemically neuter your dog without surgically doing it. They use it in breeding dogs...you can discuss it with your vet. Proscar is the drug and it is among the safest in this situation.