Are you trying to adjust the cone while the wheel is on the bike? I take off the wheel to do the adjustment. This allows me to use a cone wrench on the cone and any wrench, regardless of thickness, on the lock nut. My cone wrench is a Sunlite combination CW, lock ring tool, and chain whip. It's 4mm thick and works great. I use an ordinary adjustable wrench (or any wrench with the correct jaw opening) on the lock nut.

FWIW, I check for proper adjustment by twirling the axle ends while the wheel stands on the floor. I loosen one lock nut and manually tighten the cone until the bearings rumble a bit. It's felt in the fingers. I then back off until the rumbling goes away but I can't feel play in the axle. Then I tighten the lock nut and reinstall the wheel. It pays to check the bearings again by feel after some riding. (I believe this is all per Sheldon Brown.)

Properly adjusted, a mounted front wheel will have zero free play but can be spun manually and continue spinning by itself for a couple of minutes. You'll get tired of waiting for it to stop.