To my knowledge the only way to quiet the router and cutting noise is to fully enclose the machine. The enclosure will need to be lined with sound absorbent material and the enclosure must be easily removable for maintenance and alignment. The dust collector (or vacuum cleaner) will still be almost as loud. It will get very dirty inside the enclosure.
I plan to build a sound deadened room for the cnc router and dust collector when my workshop construction is completed.