It's time for my annual period of feverishly looking over this game trying to find something new again.
Turns out, you can optimize walking down stairs in a number of ways:
1.Walk over the stair entrance by holding Up to walk over the edge and start falling on top of the stairs
2.Continuously jump down the steps. Saves a frame each time it's done.
3.Drop into the screen transition trigger from above.
Saves around 13 frames on this staircase.
Make sure to hold B when grabbing the staircase again so Simon does not walk upwards for a frame first. This is how the second technique can actually save time. Alternatively, throw a subweapon instead to be able to drop again faster. The second technique is also subject to subpixels which might influence the time save somewhat. It's unfortunately pretty rare for stairs to be arranged the right way though, so the total time save is probably quite small.