The little parasene weed wand is frankly useless. I've got the weed wand professional which is another ball game. It's great for knocking back weeds where hoeing isn't an option ( on gravel for example ) and a couple of visits does pretty much take a redundant allotment back to bare soil. It does have 2 advantages not enjoyed by roundup. It kills weed seeds on the surface and it leaves potash. Of course if all you're bothered about is killing weeds then glyphosphate is fine, unfortunately I choose not to use chemicals so this is the only real way.
As regards paraffin it's not really that difficult to find. If you don't mind being ripped off then the B & Q's etc sell it for about £4.20/5 lt. Some garages likewise. We have a local garage that still sells in bulk and it works out around £3.20/5lt. We sell it in our lottlie shop for that price as well