This is not something I recommend.  I like 'clean' two-stage military triggers, like the Krag's, '03 Springfield's, and M1 Garand's, especially at the range.  It is nice to have the safety of a deep sear engagement, take up the initial slack, and have the trigger "break" cleanly at 3 to 4 pounds.  However, "back in the day", when two-stage triggers were new, riflemen did not like the long "Drag" ('The distance through which it is necessary to pull the trigger before the gun will be discharged') of the Krag.  Competetive Shooters were use to the trigger pulls of the Trapdoor Springfield and commercial target rifles.  Walter Guy Hudson pictured this home-made device, trapped under the Krag trigger guard, to eliminate the 1st stage of the trigger pull.  I've never seen one in person but I am sure someone will/has encountered one.

I like the two stage trigger and wish my Krag had a decent trigger pull.  Of all the M1903s & Garands I've seen, my M1898 has the worse trigger pull of them all; rough and heavy.  The sear is nice & smooth so I can't say why the trigger pull is bad, it just is.

Please excuse my ignorance, but I don't see it on a Krag breakdown parts sheet. When you say "trigger spring" do you really mean the small sear spring?