I have a Shopmate radial arm saw with a router outlet spindle. I can not find a collet chuck attachment to perform routing. Is it possible and save to attach a normal drill chuck to perform routing work at 20000 rpm?
No. A drill chuck is designed for perhaps 2000rpm, 1/10th of your spindle speed. It’s also designed only to take a compressive axis force, not longitudinal forces, or the (if you get something wrong wrong) axial forces pulling the chuck from the spindle. Anything going wrong at 20,000rpm is extremely high energy, so it’s not worth the risks. ER16/20 etc collets are available cheap on eBay and are intended for routers.