Welcome to the forum JeffS.
No direct experience of Blu Thru, but I've used Salt Away solution before. I assume they both do the same thing. If your boat is garaged then there's no need to fully winterise the engine. If it lives outside under a tarpaulin, then yes winterise.
I've looked at injection systems for the solution if running on muffs, but quite honestly, a flush bucket will be less hassle. Run the outboard with the solution for a good 20 minutes until it's up to temperature. You can hose down the sponsons afterwards, but no reason for them to be touched, as it's just the telltale outboard stream. Remember and top up the water. My Tohatsu pees like a shire horse!
I'd remove the thermostat afterwards. You can lightly brush and salt build up off it with a soft head wire brush. You'll probably need a new gasket when refitting.
Remove the spark plugs and spray fogging oil into the cylinders.
Also drop the gear oil. Any water in there then you risk cracking the gearbox if there's a hard frost. You can fit a new impeller for peace of mind. Straight forward process then refill with fresh oil.
I also spray 3M white grease on the linkages to avoid corrosion issues.
Given engine is new to you, remove the propeller. Good opportunity to grease the splined shaft and check there's no fishing line back there. You'll need a new propeller split pin. Ensure it's stainless steel.