Remembering back to the one my parents had I would have initially said 5/16.
After a bit of googling I found this reference
https://www.breezedryer.com/images/P...ist_Manual.pdf
At the bottom it lists the case bolts as part FD900738 but cannot find specifications.
Looking at the other bolts listed the threads are all BSW.
My guess would be 5/16 X 1 inch BSW hex head, but this is only an educated guess.
The green shed and other hardware stores usually have a selection of 5/16 UNC and UNF or could be swapped for 8mm. Plenty of selection of imperial and metric in other sizes as well.
The hoist is remote from you but is the hoist remote from hardware stores ?