just be yourself. Most people probably wouldn't bother you. Maybe some will be interested because they are star trek fans. If you are very self-conscious it might be a problem since you would probably get some weird looks and some people might laugh. Overall, though, I think most people would ignore the costume and and treat you normally. If muslims can walk around in public wearing traditional clothing without a riot breaking out then so can you!
I would suggest attending more conventions where this sort of dress is deemed more appropriate and interacting with other fans if you are trying to enhance your social life. Also, start posting here on the BBS more. You can make lots of trek friends here. Welcome aboard!