I'm simply wondering how people sanitize their auto siphons. I usually try to get a little starsan up above the plunger, so it doesn't stick, and then I put both ends of the siphon in 1/2 gal of starsan. I pump through the system to sanitize the inside tubing. I spray the outside quite well with my spray bottle and proceed to rack. I always think I could do a better job with sanitizing the outside. Maybe there is some way to soak the outside without some special tupperware and without spraying more sanitizer on the floor than anything.
I do the same as you to sanitize the inside of my auto siphon. For the outside I use a non-abrasive sponge that's been soaked in my sanitizer (usually iodophore, sometimes starsan) and wipe it down.
I use a paper towel soaked in iodophor solution to sanitize the outside. I also find the pump & clean method doesn't always get all the nooks and crannies clean so I disassemble mine, soak in oxyclean solution, and run brushes through it to get everything knocked loose.
I think what you're doing should work fine. But here's what I do: I usually keep a five gallon bucket of starsan around--using distilled water and keeping it in a covered bucket, it retains effectiveness for weeks, probably months. I'll separate the two parts of the autosiphon, dunk 'em in there, flip 'em over after couple minutes, then hook it back together, put the tubing on, and pump sanitizer through the whole enchilada.
I use a spray bottle. Spray the inside of the cane from both ends, then the outside. Spray the outer hub from the top down into it, then on the outside. Spray the outside of the hose. Spray both ends of the hose on the inside and swish the starsan around a little. Done.