Adjusting valves isn't exactly a bad idea, but probably unrelated to the noise. If your cousin's a master tech, he won't screw up your engine by making the valve clearances too small. The worst thing that can happen is he'll measure them & find they're just fine. Then he'll tease you for wasting his time or your money.

Have him listen to the noise. A good tech can easily tell the difference between the sound of valves (out-of-adjustment) vs. a starter that isn't disengaging. We can't actually hear it from here.

BTW; adjusting valve clearance has nothing to do with clearance between the piston & the head! (?)