Thank you for your question, @espectros
The best brush for this would have harder and thin bristles, and the brush should be used dry in most cases. However, if the grime needs some dilution, you can use IPA (Isopropanol). But if you use IPA, please remember to be in a well ventilated area, and use a mask (ideally with an activated carbon layer). If it’s not a dry residue, I recommend the vacuum technique.
I do not recommend water because it may dilute the grime but keep it in the skin, now in a wider area. If you ever need to dilute the grime, it needs to come off immediately, avoiding spreading at all costs. If badly handled, a small spot diluted can become an ugly wide stain.
Regarding brushing techniques, you should go with the grain, either with the bristles perpendicular, or at 45 degrees going against the brush movement in order to lift the residue.
You can also use a percussive technique, simply banging the brush against the skin. For this to be effective, hold the handle by the tip actuating it with fingers and wrist, and do a wider arc to gain speed at the tip of the brush. The impact of the bristle against skin should be sharp, quick, but low pressure (as a finger flick, low pressure and sharp, versus a punch, high pressure and blunt).
Now that I mentioned flicking, that is also a technique to try to dislodge some dry residue. Flick the skin hard with your finger. Alternate techniques to try to weave the residue out.
Let me know if you have any further questions.