Rich,
In your particular situation, I'd go with a # 28 if the screw diameter is truly .138". A #28 is .1405". A 9/64" is .1406".
A lot of times I will go to a zero clearance fit and then diamond lap the hole, especially on tumblers and frizzens where a tight tolerance is critical.
David
I make all my own screws for locks.My 6-40 is .130-.132. The 5-40 which I seldom use is .120-.122.
Bridle screws are .108-.109 and a #35 drill is .110. Sear is REAMED .1094 and screws are .109.
I finished a Rigby "4 pin" recently and the sear turns on a polished drill rod pin of .1094 thru a .1094
hole. With the rigid bridle and a properly cut full cock it is a very stable assembly.
Helpful hint. Any reaming must be done with a sharp reamer and flooded with cutting oil or one of
the commercial tapping fluids.
Bob Roller