Lawman,
I'd expect no problem using monometal bullets per se.
Considering that you mention a Mannlicher 1903 the only issue might be the cartridge OAL and nose profile to get the bullet to feed reliably thru the rotary magazine and feed ramp.
My 1903 is pretty picky unless a bullet (like the Hornady 160 grain round nose) that matches the period originals is used. Likely for a similar length and profile a Mono will be a bit lighter.
My rifle does not even like the very similar Privi 156 grain semi round nose because of the round nose having a small flat tip. They shoot fine but feeding smoothly is problematic.
I have no idea who might make a 6.5 mono that would solve the possible feeding issue in a 1903.
- Mike