I take it you have no draincock? If you do, I'd use that. Detaching the bottom hose is going to cause a torrent of coolant to come out, leaving you with air pockets in the motor that you won't be able to eliminate with a garden hose. I wouldn't run an engine under those conditions.
There are also environmental problems. Coolant is very toxic. You should catch the coolant and recycle it, or at the very least, pour it down a sanitary drain. With your plan, it'll be difficult to catch everything coming out of there.
I think an ideal plan would be to locate the block drain, then drain the block and radiator, which will get everything out, run the engine up to temperature with some fresh water, adding some radiator flush chemical if you prefer, or not, then drain and catch all of that, then refill with coolant. I know it's not as simple as your plan, but IMO it's the right way to do it.