You're idea is good! Will start doing this tomorrow. I use a plastic measuring cup to pour very hot water into my Q-shave scuttle, and then clean the razor. I had been swishing the razor in the sink.I do have a couple of lather bowls and soap dishes, but the mug in my bathroom is for rinsing my razor in, so the sink water stays free of stubble for face rinsing.
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How do you use yours?
That!One mug is used for soaking the brush and wetting the tips.
Three other mugs hold soap pucks for loading/lathering.
I load the brush in the mug and then face lather, with the exception of Williams, for which I load the brush and at least begin to build the lather in the mug. For most soaps in a mug I load the brush for 20 seconds or thereabouts, while with Williams the brush is in the mug for at least a solid minute, often significantly longer, with a few drops of water introduced to the mug a couple times. When I take the brush to my face the Williams lather is lather, but it is still a little pasty, so I add a little more water and continue building the lather on my face. I've done it this way for well over 40 years. Most of the problems that today's shavers have with Williams stems from the fact that they don't know really understand to make lather with a "mug" soap.