Hey Lorenzoid and thanks for the tag. I will try to help if I can. We just lost our pet today and I am low on sleep so I my thoughts might be a bit scattered.
If the OP had come to my office with this I would have told you to clean it daily with warm soapy water and keep covered with bandaid. And to stay out of any “dirty” water like streams, lakes, hot tubes and yes, the ocean. But divers being what they are I know most would ignore this advice.
It is hard to tell from the photo but I think maybe it is not too deep? Of course any break in the skin is a portal for infection.
Sites more distal to the heart do have a greater risk of infection. Age and health also play a role.
As for ointments, I usually recommend polysporin or equivalent for at least the first few days, especially if I feel there is a more than average risk of infection. But I know some dermatologists that recommend vaseline for low risk wounds. The purpose here is to decrease infection but also to keep the wound base moist. Scabs slow healing as does a dry wound. Broad spectrum antibiotics and drug resistance isn’t really a part of this discussion, yet.
As for sugar and betadine, we stopped using chemicals on wounds many years ago. If a wound is particularly contaminated I might use a half strength peroxide mix briefly. The problem with betadine, alcohol, peroxide, is they don’t know good from bad and will destroy indiscriminately. All that is needed for most wounds is clean water.
As for sugar, I have never recommended it’s use. I have seen a honey paste used for dirty, necrotic or slow to heal wounds but not routinely and not for clean cuts.
IF you choose to dive with the cut make sure you clean it very well after diving. If you can manage a waterproof dressing all the better (and yes here a sock might help protect the dressing). But absolutely keep a close eye on it and seek care early for any signs of infection.