I have three chromatics - a Swan and two Hohners. On all of them, the sticky slide problem is due to dry saliva. Try blowing up and down the harmonica without using the slide and then try (gentle) pressure on the slide. This might take a while! I find I have less issues if I put the the chromatic somewhere warm and dry for a while after I’ve finished playing - but occasionally give the slide a push while its all drying out. Next time it will be much less likely to be stuck!
Hope that helps
Cheeers
Maka