Right, kiddiwinks.
New release for y'all - v6.3.1 has just been released in the last 48 hours, although the AppImage download is still sitting at v6.2.0. So; I've d/l'ed the .deb, extracted it followed by re-building into an AppImage via the use of Fred's scripts, and then building a new format of 'portable' I trialled earlier on today.
AppImages are a great way of using apps, but they do have the nasty habit of leaving config files/directories behind them wherever they're run. So; to make these truly portable, I've combined the best of the AppImage AND my standard 'portables'.
The portable directory now contains just two things; the newly-built AppImage and a 'LAUNCH' script. At first run, because this is in fact an Electron app, you can use regular Chromium browser '--switches'.....with the result that a 3rd item, a 'PROFILE' directory, will be created beside the first two. Second & subsequent runs, OnlyOffice will then use this self-contained config profile. No more 'stray' config directories sitting around all over the place..! 
You can of course share a common profile between multiple Puppies on the same machine, but you then need to start all over again with another 'common' profile when moving to another one. Like this, you can run OnlyOffice from a flash drive.....anywhere you want.
You can find this new portable at the link in post #1, above.
As with all my portable builds; d/l; unzip; move anywhere you like - preferably outside the 'save'. Click to enter, click 'LAUNCH' to run. This takes a few seconds before things start to happen; it's a BIG office suite, and has to unpack itself into /tmp before firing-up.
The beauty of this layout is that once you have the portable directory, to keep up-to-date simply visit the website in post #1, d/l the newest AppImage, unzip & re-name it to match the existing one (you can rename these to anything you like, as it's the 'act' of clicking on the outer directory that transfers the executable action to the "AppRun" script within. The actual 'label' is in fact irrelevant..!) Then just swap old for new.
See what y'all think. (Oh, & BTW; this new release now has a much needed 'dark' theme....)
Enjoy.
Mike. 