My oldest child >never< drank formula - not once. We tried every brand out there, powered and ready-to-serve. He didn't take any of them. It wasn't too much of a problem because I had planned on breastfeeding for awhile anyways (he stopped around 15-16 months). By 6 months it was much easier to leave him because he was eating other foods. If you are only going to be gone a few hours, just have the sitter feed him pureed or fork-smashed foods and not worry about the formula/breastmilk. (I could never pump, either). Our kids were also drinking for a sippy cup (we had to hold it for them for the first couple months) by 4-5 months old (my son never took a bottle, either) so he would drink water at meals when I was gone and the sitter was feeding him so he'd get some liquid.
And don't feel bad about skipping a nursing session once in awhile. Doing it once in awhile won't hurt your milk supply at all at this point. Maybe in the first few months, but not now. You may be uncomfortable, but by 6-8 months I was never engorged by skipping a feeding -- your body will adjust. And I had more than enough milk - all my kids breastfed until at least 15-16 months -- some almost until their 2nd birthday and we never had any problems.
Some people say 'rearrange your schedule'.... well... you are more than just a mom to that 1 baby. You are a wife, maybe mom to other children, a woman with friends and a life and an identity. You can't be expected to be around your child 24/7 for an entire year without losing your mind and losing the intimacy with your husband. In the old days, moms had nursemaids so they could leave and get a break now and then - today we have formula and pumps.