I brew at work all the time with an AeroPress or Clever and a $40 Hario Slim grinder. While the particle size varies quite a bit with most hand grinders, it allows me to grind + brew fresh coffee, and enjoy it throughout the day. You could invest in a sieve (Kruve or similar…) if you wanted, but I find I can remove most of the ‘fines’ just on a standard paper towel before transferring to my brewing device.
In a pinch, I’d prefer to grind, seal, and then brew when needed as opposed to brewing into a thermal flask and letting it sit for any length of time. I sometimes do this to prep a V60 the night before so I don’t have to run my grinder at home and risk waking up my family as I’m getting ready to leave in the AM.