Hi,
Basically, yes, there are obviously many risks doing a fast-forward of almost 5 years, maybe even more with a project as active as Jenkins :).
BUT, depending on your environment (how many jobs, nodes, exotic configs, unmaintained/custom plugins...), this may not be a so big issue in the end.
The upgrade should still be pretty automatic if you're a bit lucky.
No specific patch or something should be required off the top of my head.
What you want to do is to replicate your whole current install the new target server, and just try upgrading. You'll see how it goes. Crawl the archive here about how to move a server onto another machine about that (basically, rsync should almost always be sufficient from my experience).
When you have done that, and have found specific issues, don't hesitate to come back here to ask for help/advice.
HTH
-- Cheers