The problem behind his refusal may be due to intense food preferences or a need for consistency regarding meals, or possibly just a rejection of smell, taste, or texture of the laxatives. I had impacted bowels as a small child, and had the usual enemas and suppositories to get and keep things moving.
If you can change his diet to include fruit or high-fiber grains/vegetables, that would likely help a lot. If you can find out what the source of his resistance is, so much the better.
Some Aspies respond very quickly to direct orders from an authority figure. If his doctor tells him straight out to take the OTC remedies, perhaps even a daily fiber supplement, he may comply.
Also worth investigating is the source of the constipation. Possibilities include diet, stress, and the other obvious factors.