Don't know what a pachymeter is but with a vernier caliper just get a bit of wood that's thicker than the ledge.
Hold the wood against the transom on the ledge side of the transom with the wood sticking out beyond the ledge.
Measure the total thickness of transom and wood combined with the vernier caliper & note it.
Remove & measure the thickness of the wood & note it.
Subtract the thickness of the wood from the total thickness & that's the thickness of the transom.
If you haven't got a vernier caliper then an ordinary pair of calipers used with a ruler will work.
At a push careful use of a ruler would do.
ETA. Having just looked up 'pachymeter' I now know what one is. Every day's a school day