After all, this is EXACTLY what the 4E system is. A singular set of game mechanics... sometimes narrated as "magic"... and sometimes narrated as "mundane". And thus the power-level of both sides are ALSO exactly the same as the characters level up, because they are using the same exact game mechanics and are just changing the fluff. You don't need two separate systems to accomplish it. You just need the one. As 4E PROVED to us in spades. So just use it.
This is probably a great product for some enterprising DM's Guilder to write. Re-do the 5E spellcasting cantrip and slot system as a weapon-using maneuvers combat system. Keep the game mechanics exactly the same-- each warrior has two to four "at-will" maneuvers (IE cantrips) and a whole host of of other maneuvers that require energy to do-- energy that just happens to match up with the spell slot system (or if you wanted, the spell-point variant in the DMG). But every single "maneuver's" fluff is newly created and written out as a weapon style attack, or a inspiring shout, or a combat stance. Whatever the author wanted to make these game mechanics have a martial flair rather than a magical one. So for example...
At Will Maneuvers:
Lantern (Light)
Duck And Cover (Resistance)
Alchemical Acid Vial (Acid Splash)
Quarterstaff Master (Shilleleigh)
Arrow To The Knee (Ray of Frost)
1st level:
Bolstering Shout (Bless)
Bind Wounds (Cure Wounds)
Hustle (Expeditious Retreat)
Hunter's Mark (Hunter's Mark)
Improved Disguise Kit (Disguise Self)
Improved Parry (Shield)
Commanding Presence (Command)
Heroism (Heroism)
2nd level:
Spinal Shot (Hold Person)
Fast Dodge (Blur)
Improved Climber's Kit (Spider Climb)
Holmsian Investigator (Locate Object)
Interrogation (Zone of Truth)
So on and so forth. The maneuvers are rewritten with new "non-magical" fluff... but the actual game effects remain the same. Do this for all 9 levels and create a whole bunch of warrior classes that use different "maneuver" lists. And boom... you've got a martial equivalent to spellcasting.