The clear coat on carbon is for more than just looks. It's there to provide a first line of defense from scratches and shallow dings that would otherwise cut into the carbon fibers themselves and compromise the fork's stregth. So if the fork you get is truly raw then you need to put something on there that has some significant thickness. Ideally that would be a thin coating of some epoxy resin that is resistant to scratches and dings to act as an armor coating. This can actually be done but it's a crap shoot when you don't know which resin was used for the carbon layup so that they would be compatible to get a good bond and to coat it evenly. All steps that sound a bit tough given your stated troubles and lack of gear.
So in this case I'd suggest using about 5 to 8 coats of an oil based polyurethane clear varnish. If you get the semi gloss version it'll give you the sort of matt sheen that it sounds like you're after. If it's too dull you can mix gloss and semi gloss to achieve whatever final look you want and since you need to build up the protective coating with multiple coats you have some room to experiment on the first coats to get the sheen just right.
Use an oil and wax autobody prep solvent to clean the carbon layup before applying the first coat and do not even touch the carbon or in between coats without wearing latex or nitrile disposable gloves from that point on until all the finishing is done. A good quality varnishing brush will do just fine for applying the varnish. Adding about 10% mineral spirits to the varnish to thin it will allow it flow out so it's smooth like glass. From there you just need to learn to brush properly. I'm sure there's some guides around on the net about varnishing boat wood "brightware". Look them up. In any event the key is to lay the varnish on and even it out and not to suds it up with excess vigorous brushing. Done right the results will look like they came from a spray gun handled by an expert. To deal with the inevitable dust spots wait for a couple of days before the last coat for the varnish to harden up well and then wet sand with 400 grit to remove the dust bumps and to lightly dull the rest of the varnish. Then lay on the final top coat in as dust free a location as you can.
Because you'll be brushing the varnish on you could actually clean up a room top to bottom in prep for this by wet toweling the wallsm ceiling and floor to remove all the dust. Wet rag the furniture or remove it as well. And obviously no rugs or stuffed furniture in the area. Wear freshly cleaned clothing and don't scratch your head...
When in the room move slowly so you don't stir up the air. Do all that and you may well not need to deal with any dust or at least it'll be only a very few spots.
The varnish is going to take some time to dry to full hardness