I did this earlier. Was in the same situation as you (on 4.82 HAN, wanted to update to 4.84.2 HFW to try out HEN.)
Anyhow, this is exactly what I did. For the record, I too have a lot of games installed. I didn't lose anything. I also did NOT install it twice, was advised not to and that it's pointless unless you want to do the CFW thing.
- I downloaded the HFW. Made a folder on my FAT32 USB called "PS3" and inside that folder another one called "UPDATE" which is the folder I put the PS3UPDAT.PUP inside (Be sure to rename the 4.84.2HFW to just "PS3UPDAT.PUP")
- Copied the "hansupportfiles" to the root of my USB.
- Went to update via storage media [be sure you don't have ANYTHING plugged into your USB slots other than your Flash Drive, I had a USB controller connected and while trying to update I got a copy error. It was fixed by unplugging my USB controller and just using a BT one] allowed the system to update and shut down automatically afterwards.
- After the HFW was successfully installed, I went to web browser > **ps3xploit.com >Domain no Longer owned by team** (ps3xploit.me =new) > HAN Installer. (set the HAN installer page as your homepage if you have trouble initializing it.) after the installer initialized successfully, I clicked on "Install HAN" and bam it installed and my system reset.
- Deleted my old HAN Toolbox (located in game data under the game tab)
- Enabled HAN one last time from **ps3xploit.com >Domain no Longer owned by team** (ps3xploit.me =new)
- Installed the latest HAN Toolbox.
- Done.
I haven't gotten around to testing out HEN yet, despite going through the effort of updating to HFW. Am seeing and hearing that there's lots of compatibility issues and bugs (blackscreens, freezing, system going to recovery mode, bricks?, etc.) not really wanting to risk my only system for it yet. Was advised to wait for updates, would probably advise you to wait a minute for some updates too. This appears to be quite new and imperfect, so hopefully any of these problems get fixed soon so we can all try this out without wrecking our consoles lol.