Officers apparently did not wear these. Officers either wore Bersaglieri or Chasseur caps, on their preference. No photographic evidence to go on. Reports indicate that the men's clothing was in miserable condition in April, 1862. Definitely NOT company letters.
Bersaglieri hats show the cut-out eagle remaining.
No clue what officers wore. Presumably, they purchased and wore regulation uniforms. Presumably, the appearance of the unit throughout the rest of the war was largely indistinguishable from the rest of the Army of the Potomac, except for a few, rather dilapidated Bersaglieri hats amongst the surviving veterans. Almost all of the latter did not choose to reenlist in 1864. Corrections and suggestions welcome.