I would be very open and direct about the accommodations you need. This is food for your baby. The baby can eat one of two things: milk or formula. If you want to feed them milk while you're at work, you need to be able to pump. In order to get enough milk for the day of daycare, you may need to pump three times or more, and those pumps may need to be longer than 20 minutes. It also takes 5 or 10 minutes to set everything up and break everything down. You can't expect to get enough milk with a couple little 10 minute pumps. If you pump that little, your supply will drop.

In addition to ideas you've got like calling in from another room, you could get an in-bra pump. I had a Spectra with my first kid and it was great, but not subtle. This round, I have an Elvie stride. It's awesome! It would still be awkward to sit and pump around people with the stride, but you could do it. I've worn it on errands, to a wedding, etc. At the end of the day, again, this is food for your baby. So awkwardness be damned.