This is a good first issue to start with JabRef. Apparently, this was how I came into JabRef development in early 2009. On 2009-03-26, I submitted the patch 114 (https://sourceforge.net/p/jabref/patches/114/) to the sourceforge tracker.
In other words, if you know someone with a bit Java knowledge, this could be a way to introduce him into JabRef.
I personally currently have no time to do it for myself. So many other promises made.
@mvalle This feature is available in the latest JabRef 5.15
You can set a custom cite command in the preferences for Push To Application and then this will be used when you select the option from the context menu: