This is what I use as a sleeve holder. You insert the sleeve into the opening, then use rubber bands to secure it to the arms. I go a couple steps further in securing it from moving out of the holder during fast action, which I can describe on request, but that’s the gist of it.
I don’t use the Handy, though I have one and have used it in the past with sleeves at least as heavy as these, using the same sleeve holder with the Fleshlight adapter that the company designed (it replaces the strap). It will build up heat faster than with a lighter sleeve, and probably moves a bit slower, but it works. It will operate for roughly an hour under those conditions with a typical active script, before it stops to cool down.
I now only use a customized OSR2+, which has no difficulty with the sleeve weights.