You can actually probably do the Schilthorn AM excursion and then still walk Mannlichen to Kleine Scheidegg in the afternoon.
On my tour, the tour guide offered to take anyone who wanted to go up the Schilthorn on the first gondola up. We did that and then the bus driver met us at the gondola (which was where the bus was parked overnight anyway) and drove us in to Lauterbrunnen. The guide coached us on what tickets to buy and got us started on the Mannlichen-Kleine Scheidegg hike. He went with us but hiked very fast while the rest of us spent time with our jaws dropped open. The bus met us after we took the cog train back down from Kleine Scheidegg and transported us back to our lodging which was at the end of the valley at Stechelberg. I'm not sure if that tour still stays at Stechelberg or if it is staying elsewhere.
Your guide will discuss your options and give the group advice based on weather. Some offer to take you up, others might not. It's a day on your own so if they offer, take them up on it, lol! Don't lock yourself into a decision on this now. Wait to see what is going on.
BTW, I'll also suggest that ANY thing extra your guide offers, grab it. Our guide also offered to organize an extra dinner and a wine tasting which was not covered. He told us how much, we paid him, he paid the restaurant/wine bar. It was a good deal.