Sure, as long as it's dry. I use a carbon fiber brush just before playing also.
I made mine from the T-shaped attatchment and used painters pad made for doing your trim or edging, as it's a bit more "bristly" to get into the grooves.
The record needs to be dry and although it looks fairly dry after vacuuming, it's still a little damp. Give it a few minutes. I don't know where you live or how good your vacuum was at getting off the water but make sure the record is completely dry.
Something I found that works to more easily replace the velvet, paint pad, whatever material surrounding the grooved-crevice tool:
Duct Tape!
Put a layer of duct tape covering the crevice-tool slot, cut it to reveal the slot. Hot glue whatever you're using as a cleaning fiber/pad/material to the duct tape itself, then when it gets soiled just peel the duct tape + whatever-material off in one fell swoop.
I learned this the first time I tried to peel off strips of paint pad I'd adhered to the crevice tool with hot glue. Today's hog glue is NOT yesteryears hot glue formula and is way more permanent....thought I was going to have to make a new crevice-tool adapter at one point when the damn hot glue wouldn't come off cleanly.