I've been in the receiving and the offering side of hand me diens. When offering, I didn't want to be pushy either, since some people prefer to have all-new stuff, and some are leery of hand me downs for whatever reason (fwiw, on a few occasions I have accepted bags of hand me downs only to find that stuff wasn't laundered or was so worn or stained as to be unusable, so I understand the possible reticence).
I also got offered a ton of stuff for each child and it was always framed as, "I have XYZ to give, would you like it?". If yes, then we arranged a hand-off time. If not, no worries, the stuff would get offered to someone else or donated. In each case it was pretty casual.
Since your brother has already said they'd be happy to have the stuff, i think you could just send a txt/email or call and say hey, about those hand me downs, when should I deliver (or do you want to pick them up)? Even if they get a lot of stuff at the shower, sometimes duplicates are very helpful (two car seats if there are two vehicles), and some things you can never have too many of anyway (onesies, burp clothes).