Don't worry about bleeding. Usually no need to interfere with the hydraulics at all to clean up the sliding mechanism.
It would be handy to have a solid box or something similar, the height of the caliper off the ground, to give you a solid surface to work on.
And whatever you do, don't separate the two halves of the caliper - that's not necessary either.
Just as a safeguard, make sure there's no way you can accidentally press the rear brake pedal - just in case......
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