Go for a 240 grit then.
A cheaper version will something like the following.
I haven't use the above though.
I recommended a flexible mesh because it is less likely to clog. When abrasives clog, the clogs can rip the surface of the paint.
You could try a stearate coated silicone carbide paper. The stearate coating reduces the friction when sanding. Typically, they are grey in colour and the backing paper is quite/very thin. I would avoid aluminium oxide papers (typically red/green/yellow). The backing paper is too rigid. Wet and dry paper might work if you are very gentle, but if using it dry, again there is the risk of cloging.
Waterbased paints are a mare to sand, even when cured. If the grit number is too low, the paint will shear off the surface or it will clog the abrasive.
In general, when sanding existing paint work try to go no finer than 360 grit. Any finer, you risk polishing the paint and reducing adhesion. That said, if the paint is relatively new, you might "get away" with it.