The entire process needs to be conducted in pressure vessel in order to carbonate the sorbet. It would need to be similar to a sorbet keg! The slushee stufff needs to be able to absorb the CO2 and then not immediately lose all of the carbonation. You will have to maintain the finished mix under pressure until it is served in order to keep any dissolved co2 in the mix.
With the correct cryogenic alloys your mixing equipment won't blow up, but then those alloys aren't cheap either.
With the correct cryogenic alloys your mixing equipment won't blow up, but then those alloys aren't cheap either.