Can I put a 9mm axle hub with a Shimano roller brake into a 3/8" fork?
Any free space between axle diameter and clearance width of dropout sides can exacerbate problems with maintaining the correct tension between the dropouts when the wheel is installed. The last thing you'd want is to hit a bump, pothole, etc... have the front wheel fall out of those dropouts and put you into a faceplant or worse. Bikes are subjected to immense levels of vibration on every ride and those vibrations will work to loosen any weak fasteners. BTDT

There are aftermarket spacers designed for MTB applications that will adapt a 9mm skewer to a 10mm hub/dropout (typical of rear dropout clearance) and that 10mm converted to inches is .394" (3/8"=.375")

You might also find some aluminum or steel spacers at a local hardware/home improvement store. Measure out your skewer diameter and dropout width to be sure of what you're looking for.