I used to get shin splints from running, especially in boot camp when they issued those horrible cheap gym shoes with inadequate support. As soon as I could get back into my own shoes or boots I was fine.

For years my favorite running boot was my old pair of Herman Survivor hiking boots, which I still have 45 years later. Boots can be useful for relieving some impact injuries because they force a fast shuffling gait -- variously known as the recon shuffle, paratrooper shuffle, etc. It's more of a fast walking double-time with little elevation of the foot, minimizing heel strike. It's difficult to "run" per se, in boots, so it forces adopting a style with less impact for recovering from shin splints and injuries usually caused by impacts.

But I can't recall ever getting shin splits from cycling. It's primarily an impact stress injury. It might be possible to aggravate shin splits by pedaling on the toes, or ahead of the ball of the foot, especially with poorly placed cleats in clipless or cleated toe clip shoes. I prefer my cleats well back behind the ball of the foot, closer to the arch.