If you add an enclosure with an acoustic lining then the noise will be reduced, but when you cut the holes for the inlet and outlet fan(s) some of the noise will escape.

That may be OK but to reduce this you can add an acoustically lined pipe to the inlet and outlet with ideally at least one 90 degree bend in it. This will allow the air in without too much restriction, but absorb most of the sound which escapes through the holes.

Another option to help is fit a water cooled spindle instead and have the radiator / bucket outside the enclosure.