Hi, FMrsH -- First of all, I really commend you for your dedication and compassion for all those whose lives have been touched by cancer (which is practically everyone in this day & age).
Reading your post, I am not exactly sure what your FH is unhappy about. Has he explained his viewpoint to you? Is it that he'd object to your being involved in any volunteer activity that would take time & energy away from him? Or does he feel threatened by the idea that you could be collaborating on the committee with other men who might get a crush on you? Or does he have a specific issue against Relay for Life?
I'm not necessarily asking you to spill personal information here, but if you and your FH are clear on why he objects to your participation, and why you feel strongly about participating, then you are at least in the good position of communicating your values and priorities. If, OTOH, it's just a disorganized week of fighting without each understanding where the other person is coming from, then your chances of resolving it are slim.
I know there are some women who would say that no husband (much less a FH) has the right to tell his wife what committee she can or can't be on. This is generally viewed as controlling behavior and a throwback to the days when wives were treated as property. However, in real life, couples do try to agree on how they each spend their time and energy, so that if the wife hates (for example) her husband's serving as church treasurer, he might step down out of consideration for her feelings and just serve as a member of the church finance committee.
I hope this helps a bit. Again, sorry you are having to deal with this. But better now than after you're married.