Yes, there is. Stop doing #2.

Water is bad for the myriad small parts inside a shifter, that are easily rusted beyond usability. You are skipping waiting for a solvent to dry, for waiting for water to evaporate, which takes longer.

Spray your solvent in, let it dry (you can even blow it out with an air gun attachment, if you can't wait), then drip lubricant in wherever you can access the shifting assembly.

FWIW, Shimano's own recommendation is to remove the cables/hoods, and soak the shifter in degreaser for as long as it takes to free the assembly, then remove the residue (using something that flashes off quickly with no residue, such as denatured alcohol)/re-lube. FYI, Clean Streak now uses an oil base, so it's more or less ideal for the above step; even though it leaves a residue, that residue won't interfere in a notable way with the lubricant you spray/drip in.