I usually wipe the skimmer down as best I can to get all the loose gunk out, then run it in a bucket with hot tap water and vinegar for about 2 hours. Then rinse in RO.
For that HOB skimmer you could probably rig it on a small bucket...I use to use a short 2.5 gal bucket with my HOB and ran 50/50 vinegar to water. Granted, using 1 gal of vinegar for a single cleaning is a lot...but it allowed me to get it done in a couple hours and have everything hooked back up that same day. At lower concentrations of vinegar (~25%) I found that I had to usually run the skimmer overnight for it to come out clean.