I just had open rotator cuff repair. I want to get teeth pulled and get dentures. How long should I wait for it to be safe?

Dentures. I would check with my surgeon however i would wait until i can sit in the chair comfortably. You are young for dentures so please try and have some implants placed so that your dentures are always stable. If cost is a factor check with the dental schools.
No need to wait. No issue with oral health risk after rotator cuff repair. But, will you be able to use your arm to manage your mouth care after the extractions, etc.?
Do not wait. However, any dental work done after surgery, you must take antibiotics before a procedure to help prevent infection. Ask your surgeon for further instructions and regiment.
Ask Ortho MD. Ask your Surgeon for recommendation and schedule consult with your Oral Surgeon and the Prosthodontist. Together they can create the best plan and sequence of treatment. Consider implants as part of your treatment plans. Good Luck.
When comfortable. From a comfort standpoint, having your teeth pulled and dealing with the process of getting used to dentures requires you be able to sit in a dental chair for a good amount of time. From a health standpoint, your orthopedic surgeon should have an important opinion, so be sure to ask.