"Unfortunately I don't have the facilities at work to make the mix there. I have a large private office, but no place to clean dishes, make the mix, etc. And no lunch room with sink or cabinets."
So bring your "dirty dishes" home and wash them there. Carry a igloo cooler (small size) with you to work in the morning with all your stuff, cold pack if necessary, stash the dirty dishes in there afterwards and then take it home with you in the evening.
Get a package of unscented baby wipes, a stash of plastic shopping bags (from grocery store, etc) and use that to "wash up" and toss in the shopping bag. Tie up and toss back in the cooler.