I was hoping to get to this question last week, but was busy.
I believe I once saw a individual combat manual a few years ago, but my searches have turned up empty. There is a manual from WW1 and a manual written just after WW2, so there was some level of individual combat training.
To say that countries had a system is misleading IMHO. All the armies taught bayonet drill to some extent and some taught limited hand-to-hand, especially with a knife, but none of the armies provided universal training to all soldiers to any greater degree. Specialized units did receive additional training.
Pista! Jeff