Yes, you can define your own clipboard shortcuts for about anything. For copy-
pasting latex you may define

(kbd-map
  ("C-S-F5" (clipboard-copy-export "latex" "primary"))
  ("C-S-F6" (clipboard-paste-import  "latex" "primary")))

in a scheme session and it will work (here with Ctrl-Shift-Fx, change it to
you taste). Be sure not to colide with already existing shortcuts, because it
my be tricky to know which will be active. In order to have these shortcuts
permanently defined, you may put them in the file my-init-texmacs.scm which is
avaluated at startup. You can directly access  my-init-texmacs.scm from the
"Developer" menu, once you have activated "developer tool" in the "Tools"
menu.