Sometimes a different condom can make all the difference. There are reasons a person might not want to use protection - they might feel like you don't trust them, or they might feel offended or they might just be embarrassed. These are legitimate and very personal reasons. Let them feel what they feel, and gently explain why you want to use protection. Explain that you just want to be safe, out of respect for yourself and for your partner.
Chances are, they'll come around.
Lots of erotic things do not put you at risk for infection or unwanted pregnancy. The area under your arms is very sensitive, as is the skin on the insides of your elbows and the backs of your knees. Keeping your clothes on can allow you indirect genital contact which can even lead to orgasm, but without putting you or your partner at risk for infection or unwanted pregnancy. It can be made more pleasurable with the use of lubrication, and make sure you and your partner wash your hands before moving from one person's genitals to the other's. Learn things you never knew about what your partner enjoys, show your partner what you like.