Yes you can train Minors for that. If fact if you want to level efficiently, and control your bonuses, it's better to train your Minors. Then when you want to level, train your Majors. That way you won't get behind in the count, so to speak. You should find a balance of your Majors to Minors to level quickly at the same time. Now, what those are, and how you address them depends on your initial selection of Majors and Minors. As well as your character and playstyle.
To catch up in the count, you need to train Minors to a high point, and use those, exclusively. Until you catch up. Like if Blade is a Major at 30. And, Blunt is a Minor at 20. Use Blunt instead and raise it to 50 or even higher. That way you have a weapon that is ahead in the count, and you can play the game, until you get ready to level up.
Or you can just grind for levels, if that's that what you want. And use your Minors to get your +5 Bonuses.
EDIT : It's hard to put "quickly" and "efficiently" in the same sentence. As one contradicts the other.