I want to recruit Professor Scara instead of Dr Li during the main quest 'From Within' because I plan on siding with the Institute and I don't want to blow Li up later on.

Is there a way to get the alternate person for this quest without screwing things over with the Institute?

No, there is no way. Dr. Li won't die even after you destroy the base though since Dr. Li can be found in a closed off section of the BoS base alive. I have a feeling she's canonically alive or they just don't bother to do anything with her so they just dump her off somewhere off the map. Yeah, you need to be hostile toward the Institute before getting Dr. Li. if you want to get Scara.

The only option is to not do "From Within" since you don't intend to complete the Brotherhood questline anyway, although you'll miss out on Blind Betrayal, which is really annoying.