What I'd do would depend on what is in the shed haha
I'd use 3 ish mm braided cable, drill 2 holes in frame, securing the ends of cable with these as shown on the box
https://www.bunnings.com.au/zenith-3mm-stainless-steel-wire-rope-grip-12-pack_p4220459Before securing, would slide the hose over the wire.
If you want to be really nice to the missus, put this around the hose
https://www.bunnings.com.au/k-flex-...-pipe-insulation-suits-3-4-pipe_p4920351comes in different sizes so you would have to check