is it possible to update my trophy after hen crack if I don't enble HEN

Basically yes. You should stop unlocking trophies and syncing where the servers are offline.

It is not possible to update your PS3 trophies after using a HEN crack without enabling HEN. The trophies, especially when manipulated or synced manually, require that HEN or similar software is activated on your console. When HEN is not enabled, the system won't recognize the changes you make to the trophy files, and as a result, the trophies cannot be synced properly with the PlayStation Network (PSN).

It's safe as long as you do it the right way, people have been doing it for ages
So this is how i do it:
-Play pkg/iso etc (cracked) games offline on user, earn trophies

-Clear syscalls (triangle +r2 combo need webman)
-Restart ps3 to disable hen
-Log in and log onto psn dont enable hen/launch any homebrew just go to trophies
-Sync and either play games i own (disc/digital from psn store) or log out, go back to user to play cracked

or just order boosting through https://onlyboosters.gg/cod/cold-war/ to solve that little problem