I don't know about the Mac Bluetooth stack, but if these machines are both network-connected and active simultaneously, there's software that will let one proxy to another over the network. In that scenario, you have the associated software installed on both machines, your keyboard/mouse/whatever connected to one machine, and then hit a key combination or similar to switch, which should be effectively instantaneous.
searches
It sounds like it's called a "software KVM" or a "virtual KVM". I won't try to recommend one, as I haven't used any, but it might be a way to avoid the delay that would work for you. One example, though: