Besides the above, check the replacement skewer to be sure it fits your frame properly. Some skewers, QR and non-QR, have nuts that won't quite fit the droput lawyer lips and slow-release wheel removal thwarters. Those "safety" doodads can actually contribute to an unsafe condition if we swap quick releases. If the retaining nut opposite the QR doesn't fit completely inside the lawyer lips, it'll clamp unsecurely on the wrong part of the dropout. That could lead to a bent or broken skewer and worse.
I discovered this recently when I put the wrong QR from my road bike onto my errand bike. The road bike skewer has a fancy designed retaining nut that wouldn't fit inside the errand bike's lawyer lips. I noticed the mismatch when the front brake suddenly jammed against the rim. I knew the brake was adjusted properly so the wheel had to be off somewhere. Sure enough, the mismatched skewer nut kept the wheel from seating correctly. I have some spares so I dug around until I found a nut that correctly fit that bike.
Yeah, maintenance of bearing components can be a chore, but with a little practice it's not too tedious. The hardest part is usually tweaking the cone/cup tension jusssst-right. Usually takes me two or three tries to get it right after tightening the lock ring.
Lock nut must fit inside that recess.