Sometimes, but usually not. The limitations include the availability of cones that fit, and in many cases the clearance of the center of the hub. Start by removing the 5/16" axle and seeing if a 3/8" rod will slip through the hub, if yes, then you can start hunting for cones.

OTOH, there's usually no problem using a 5/16" axle woth a fork whose dropouts are sized for a QR axle. To ensure that the wheel always goes back on the same way, get in the habit of tightening the nuts with the bike vertical on the ground. That will let gravity position the wheel consistently.

If you still want a tighter fit, the easiest way is to make a pair of rings to slip over the axle inside the dropouts. Years ago I made a pair by cutting them off a piece of 3/8" OD copper curtain rods. They took about 10 minutes with a saw and file to make. Just be sure that they're narrower than the dropouts so they don't keep the nuts from tightening enough.