I want to send you both
. I am asexual and married, and it is challenging. I didn't know I was asexual, so it's a slightly different situation from your man who has been upfront with you--I'd been brought up in a very strict religious household in which pre-marital sex was a disowning offence, plus I'd been abused but was obviously too scared to tell my parents, so literally had no normal sexual experience prior to my relationship with a completely inexperienced boyfriend who thankfully has a low sex drive.
I'd recommend speaking honestly to him about your feelings, needs and desires. From my perspective, I am very happy to do some (non-PIV) sexual activities because my husband enjoys them, I like the closeness, and to me it's similar to cooking a nice meal or buying a treat or giving my husband a massage - I get emotional satisfaction and pleasure from his physical pleasure, so it's not a chore. For my husband, that's enough, because I'm an active and willing participant in making him feel good (which makes me feel good if that makes sense? it's not physically pleasurable but very emotionally satisfying).
However, if you have very mismatched sex drives (even average might be very mismatched for him) and this is an important thing for you, or you think it will become so over time, then I would say it's better to break it off now for both your sakes. You don't want to feel resentful/unfulfilled and he cannot change his sexuality. No matter how you dress or what you do, he won't be sexually attracted to you - it's just how it is. It doesn't mean he won't love or care for you, but if sex is a fundamental need for you then you need to think long and hard and sit down and have an honest conversation about the relationship and where it's heading.