pump area = 0.307 sq.in., so load is 0.307*120=36.8 lbs, add 10% to allow for pressure drop in clacks and friction, say 40.5 lbs. Presuming the pin is in double shear the area is 2*0.25^2*pi/4 = 0.098 sq.in, so the shear stress is 40.5/0.098 = 413 psi, which is quite low. Yield stress of even EN1A is 230 MPa, 33400 psi, and BS2573 would recommend 37% of this (as allowable shear stress, so you are well in. The bearing load is a different matter. The projected area is 3/16*1/4 = 0.047 sq.in, and so the bearing pressure is 864 psi, which is on the high side, so bronze bearing and case hardened pin would be my choice. Good provision for lubrication as well. Avoid notches/sharp edges as much as possible, and if it has a thread on the end avoid case hardening that. There are a couple of ways of doing this. One is to apply the case compound before you cut the thread, allowing it to cool slowly, then cut the thread, then get it red hot and quench, the other (which I've never tried) is to copper plate the bit where the thread is going to be. Cooling a small part slowly is not that easy either, trial and error, if you can still machine it it's ok.
I know that silver steel is the go-to material for model engineers, but in well over 40 years in industry I've never seen it specified for a machine part, except for punches, dies, trigger blocks etc for which a very hard part is needed