I went out to my pickup , which happens to be harboring 12 or so 5gal. buckets of a couple different makes and took a look at them.  They all have  a' box' of sorts on each side that the wire handle enters to fasten itself to the bucket. The 'box' is open at the bottom. the wire could be clipped off and removed. 3/16th cable or maybe para cord could be threaded through the remaining hole , encircle the bucket  (maybe a bunch of times ... for emergency use!)  and come out the hole in the' box' on the other side.   Short loops could be formed on each side to which thicker handle material could be attached. By Johnney! !   :)                                                                              Hey,I can't wait to read,see,/hear about Martin's latest adventure!