Tell H you plan to fix the shingle, ask him what tools and materials you'll need. Tell him you're going to go for it on Sunday or something. If he chooses to jump on it before then great. If Sunday rolls around and he hasn't done anything, then feel free to address it however you want in terms of fixing it yourself.
This I like very much. I like the idea of not having to penalize myself in an effort to provide him what he needs. (I feel like it's what I did when I hired the handyman this fall, but I don't think that was received well by H or this board. I'll have to trace back and revisit that thread.)
The trick for me will be in managing to do it without sounding insincere. If I have to ask him what tools I'll need, for example, it will be insincere. I am simply more handy than him. It's not arrogance, just a by-product of being my father's daughter. Be it training or genetics, it was a gift. I'll be on the lookout for other opportunities/options.