You may just get away with your boring bar as 5/32″ is tapping size for 3/16BSF (3.97mm)
As said the reason for boring is to get a truer hole, you could also use a D bit or slot drill to finish the tapping hole.
Of course its all very well having a true tapped hole provided the thread on teh piston is equally as true, my preference would be to make the piston a few thou oversize and onve it is mounted on teh piston rod set that to run true and skim the piston to finished size.
J