What I would do is try to explain to the DM that there is no explicit rule preventing you from using knowledge skills in combat.
Sadly, however, 5e does not offer advice as to how they might be used. At my table, I have implemented a few simple guidelines for knowledge-based checks in combat:
- You can make an Insight check to ascertain the enemy's morale, as well as who the leader of the group is.
- You can make an Arcana check to see what type of spells/abilities the enemies are using.
- You can make a Nature check to learn more about enemies who are Beasts or Fey (this one is only sometimes implemented).
- You can make a Medicine check to try to ascertain how many hit points the enemy has remaining, and so on and so forth...
Just try to explain to the DM that you don't even need a special homebrew system for this to work. Skills should be able to do what they normally do, regardless of the situation. Of course, not all skills are always applicable, and there is an immense amount of DM purview that comes into play.