I would definitely worry about an oil light, unless you are just dying to do a swap. There are many internal issues that can cause an engine to die that will give no external warning until it's too late.
The oil pressure light isn't as much of an early warning indicator as it is of impending doom. It comes on with only a few psi which means the pump has stopped moving oil and is moving only air (or nothing). It doesn't take long to fry a motor with the light on (unless the switch or wiring is bad) and an increase in wear almost starts immediately.
No matter what you do, if you want it to be reliable then you will spend a lot of time or a lot of money. Everyone is keen on a turbo but then make critical mistakes like log manifolds, **** tuning, too much boost (for the mechanicals), or other engine-killing mistakes. I've been dying to do a VTEC conversion and swap for other B-motor internals. Anyone can turbo and there are plenty of examples of that. Same for H22 swaps.
Haven't seen a K swap yet- that would be pretty trick. Do a B20 to K20 swap.