My boyfriend doesn't want any general anethesia for his arthoscopic shoulder surgery. What is another alternative for this?

Regional. Regional anesthesia is an option, pending anesthesiologist review , ability, comfort and institution traditions. .
Talk to his doctor. The choice of anesthesia depends on several factors. Shoulder surgery may be done under a block with sedation or under general anesthesia. The surgeon may have a preference depending on the length of the planned surgery. Your friend should talk to his surgeon and to the physician anesthesiologist about the choices so he can make an informed decision. Get the facts first, then decide.
A regional. anesthetic called an interscalene with sedation can be used.
IV conscious. sedation combined with local anesthetic. Conscious sedation is a combination of relaxation drugs to help you relax and to block pain. Hence you are relaxed and pain free. Also post operative amnesia is a collateral benefit. Very safe and easy to monitor. Hope it helps..