I’ve done hundreds of tests on chipboard and I don’t think you’ll be able to cut without some charring, since it’s basically several plies of paper. I’ve found that cutting at power 100 and making multiple passes creates less char and a tighter kerf. For example, the chipboard I use is .08” and then .09” with the 10 mil photo paper. It will cut at 180/Full (on a pro) but it chars more and leaves a bigger kerf. If I do 2 passes at 260/100, it takes the same amount of time but a smaller kerf and less char.
I use a finishing varnish before cutting. If you’re using a photo paper, it needs to be a spray finish (lower water content - the liquid varnish will cause the ink to run when you spread it). If you’re using a canvas or rag-type paper, you could use a liquid varnish.
I cut image side up for a few reasons also. One, I feel that it makes a tighter fitting piece. Image side down will give you a smaller apparent kerf when looking at the puzzle, but it removes more material from the guts (middle portion). Two, some soot is inevitable - if you cut image side up, you can wipe down the entire face of the puzzle while it’s laying in the laser bed, after cutting, with a very, very slightly damp towel. Three, if you have pieces that don’t cut all of the way through, you can finish the cut with an exacto knife without cutting the face of the puzzle - it looks more consistent because the laser has already cut through the face.
Salt is THE way to clean the sooty edges. I think this is the main reason no one really offers laser cut chipboard puzzles (the laser cutting puzzle companies all do wood) - because the pieces do have to be cleaned and it’s an extra step in the process. I’ve used different types of salt and have concluded that the larger grain salts work just as effectively in cleaning the edges/nooks and crannies as fine grain salt, but leave way less salt powder residue on the pieces. I buy pool salt because it’s easy to find and you can buy 30-40 lb bags of it. I cut in about 250-piece segments of a puzzle (2 jobs) and clean the 250 at one time. I put a cup of salt into a Tupperware container and just roll it around for about 30 seconds.
Then, I have an IKEA kitchen utensil holder (of all things lol) that I dump the pieces and salt into from the Tupperware container. It has holes all down the side and button and the salt drains out into an aluminum pan. I have also laser cut a Tupperware lid with holes everywhere, that I can swap lids and just turn upside down and let the salt run out.