I believe (but can’t check right now) that somewhere in the NEC the disconnect switch must be rated for a minimum of 115% of the continuous load. 115% of 180A is 207A, so that would dictate a 400A Switch.
A side issue that can be a nasty “gotcha” is going to be the SCCR of the non-fused Disconnect Switch. Most are rated for only 10kA max unless fed from a SPECIFIC fuse or listed in series with a specific breaker. So if the breaker and the switch are both Eaton, they MIGHT be listed in series for a higher SCCR, but if the breaker is Sq D and the switch is Eaton, that’s not going to fly and you are left with 10kA (if you are lucky, a few are only 5kA).
To put that in perspective, let’s assume the best case scenario, your 225A breaker was put down stream of a 112.5kVA 280Y120V transformer with around a 1.2% impedance. Your available fault current is going to be around 35kA (thumbnail guess), too much for a typical NF disconnect without being series rated with that specific breaker. Most likely since that breaker is part of a larger panel board, the transformer is a lot larger and the AFC is much higher.
NF disconnects have become more difficult to use now with all the emphasis on SCCR.