Some considerations on differentials:
Open diff = equal torque to wheels Welded diff = equal rotation to the wheels
"...since you are going in a straight line."
Welded diff OK as long as rollout is matched and the straight line is the desired direction. If deflected from the desired direction by any number of possible causes, the diff will resist steering correction. Mismatched rollout (in as-raced condition, with operator weight) will induce a directional bias and imbalanced steering response.
Welded diff on a poor surface, with loss of traction on one wheel, the "good" wheel will induce a torque on the chassis tending to cause a change of direction. Open diff on poor surface, wheel thrusts are equal (assuming balanced rollout) but reduced. Little effect on directional heading.
Given ultra short Midget wheelbase, directional stability probably a plus, but hard to say welded diff wouldn't be satisfactory. On a marginal traction surface or where Hp can overwhelm traction available, either diff would produce the same thrust. Welded thrust advantage would only occur in one-wheel loss-of-traction situations.
Another consideration is how much rear axle wheel load is transferred right-to-left due to the solid axle, driveline torque, and suspension stiffness. [Who's got some strain gauges?]