Re:
OK, here's some info that will at least get you started. Firstly
https://www.cannondaleanswers.com/defin ... ain-bikes/
To fit Headshok you will need a Headshok headset similar to this,
https://www.cannondale-parts.de/epages/ ... ucts/QHDST
and a bearing seal that sits on top of top bearing, like this,
https://www.cannondale-parts.de/epages/ ... ts/QSMSEAL
and a Headshok stem,
https://www.cannondale-parts.de/epages/ ... s/QSE-90X5 I've measured 2 of the seals on the Lefty bike and the Headshok bike, they are both the 50mm seal.
Your frame is much later than the Headshok but you still should be able to fit it to frame. I've got 2 Cannondales, a Super V full suspension and a Team Blue F800 hardtail, that had Headshoks and now have Leftys. No difference in how they fit. One problem I see though is the frame was designed for a 100mm Lefty not the probable 70mm or less Headshok so could affect bike geometry. I can't see which Headshok it is but being it's not a disc fork it could be as little as 50 or 60mm. Some of the earlier Headshoks didn't even have dampers, just a coil spring with an elastomer inside it. Later forks had air springs and proper oil dampers. This website could maybe help you track down which Headshok you have,
https://vintagecannondale.com/info/headshok/ or put some more pics up of top of Headshok.
Also with the frame being disc with no mounts for V-brakes you're going to have Vs on front, disc on rear. I did it the other way round with the non-disc F700 hardtail I have I put the rebuilt disc Headshok on. Put a Magura HS33 on rear with a Magura Julie on front. Used a Julie lever for rear brake to look the same on bars, fits/works the same as original lever. It's a dry weather/summer only retro bike, me no like rim brakes in the wet.....
The internal diameter of Headshok/Lefty headset bearings is Cannondale's 1.56" size, 1 and 9/16 inches, not the 1.50" standard size so steerer is also this 1.56" size, 1.5" stems will not fit.
As to the Headshok, I'd be concerned that the boot/seal is loose, no cable ties holding it on therefore dirt/contamination may, probably will have gotten in to needle-bearings. This will kill them quickly and it's a complete strip down required to clean/replace them. It could get expensive. Several special tools are needed for this, some of which are specific to each Headshok or Lefty. I have completely dismantled and rebuilt a Headshok with a new damping cartridge. The needle bearings and bearing races were OK but the races themselves are different thicknesses to take in to account manufacturing tolerances. Each race and bearing has to go back in same position/orientation in fork or you will/could end up with a fork that's too tight or too slack to slide up and down properly. I took it apart and laid out all the races/bearings in order on large sheet of paper with each part named so there would be no mistake on re-assembly. I was OCD about cleanliness and making sure no part was misplaced/wrongly fitted.
Headshok/Leftys are not fit and forget, every so many hours of use requires the boot to be slid down and races/bearings greased with proper Cannondale grease, again cleanliness is very important.
You might find that the lower headset bearing is still on steerer as when fork is knocked out it generally stays on fork leaving cup in frame. Pull down boot to see if it's there, think all Headshok/Leftys I've got were like that. Putting the Headshok in needs a special Cannondale tool, a tube the correct diameter basically that slides down steerer driving on the inner race of top headset bearing in frame down onto fork. Most folk use a length of plastic tube this diameter. Once the Headshok is in all that is needed to hold it there is the stem, no need for loading with star-fangled nuts like aheadsets.
Hopefully the gist of what I've written is OK and somebody will correct me if I'm wrong.
