Honestly, just be the better runner and don't do it. There's no other game (that I know of) that doesn't incorporate menuing in their runs to some degree. Cheesing the system that Toast made to shave a few seconds off your time isn't the best way to go about it, just take corners sharper, find a new route, or tighten up puzzle sections. Don't abuse a system that isn't even in the game, guy works hard enough.

Big ups to CursedToast, this guy is a hero.

The route I take usually is spawn him in and run around through the film room like normal. The game will want you to take the long way to get back to the door, but you can cut back through the film room before baby gets there. When you get the fuse, go and spawn baby in the hall outside the kitchen. Stand in the kitchen doorway and wait for him to lunge, then move out of the way. The game should push him back into the wall, letting you slip by. There are some times where he will glitch out and not go through the full animation and you can slip by faster, but I haven't been able to replicate it consistently. Hope this explanation makes sense or helps.

A recent video was posted that showed if you minimize your movement and aiming, the first lycan encounter is actually faster. I haven't tried it for myself yet, but I'm willing to try anything.

I've noticed on almost all my runs that you can shimmy towards certain locked doors/gates to get closer (most winged key gates and castle doors). If you're holding forward and strafe left and right, you'll jostle your way closer to the door. This also helps with the gate in the village next to Duke. The movement seems to force open one or both doors, saving you some time between meeting Duke and getting the key.

My best time so far is 1:35:21 (NG+ Casual Glitchless Any%)