If you must stay mobile and bounce isn’t workable, the biggest improvement is to get the flash off the lens axis if possible. A TTL cord or bracket can help reduce the flat, straight-on look and red-eye. If off-camera flash is practical and won’t be in the way, even one light on a stand can look much better, but clear it with the event organizers first.

If the flash must stay on-camera, use your small softbox or some simple diffusion, but keep expectations realistic: small modifiers help most at close range. Also try lowering flash exposure/power—about -2/3 EV is a common starting point—to avoid the harsh overflashed look.

Another useful technique is feathering: aim the flash slightly away so the subject is lit by the edge of the beam rather than the center. This can soften the effect. If partial bounce is possible, even a small reflector/foamie-style card above the flash may help redirect some light.

In short: prioritize mobility and getting the shot, but improve the light by reducing power, diffusing, feathering, and moving the flash off-axis whenever feasible.