Another thing to try before opening, ja, is to work the key up and down repeatedly with your thumb at the end, holding the melodica upside down, which might loosen up anything that’s in there. You might also try something I have done when keys get sticky on my computer keyboard, which is to use a vacuum cleaner. Vacuuming the computer keyboard almost always brings something up, in my case most notoriously fine hairs from my Cavalier spaniel. When I do this, I insert my fingertip between the end of the vacuum opening and the keys to avoid direct contact and avoid too strong suction.
Also, as you look at the keyboard, are there significant differences in the gaps between keys? Some differences are normal, but it’s not unusual to have sticking because the gap on one side of the key is much wider than the gap on the other. If two white keys are too close together, you can depress each key with your thumb and gently push the other key to see whether you can reposition either or both keys so as to widen the gap. Usually you can reposition one or both keys and they will stay in the new position(s). I have evened out the gaps between keys on many vintage melodicas by doing this (either in the way I have just described or by inserting a small blade between keys and working them apart or together with sideways pressure). Sometimes I do this because keys are not depressing smoothly, but sometimes I do it just for cosmetic reasons. Be sure to do this softly and patiently to avoid traumatizing your melodica.