PANews
The blue and yellow colours are only a Home Office requirement when Home Office money is being provided to purchase a new aircraft. There is nothing to stop a police service using an aircraft of any colour when Home Office money is not involved, particularly if it is only going to be hired on a temporary basis.
Do you actually know that "KAAT want it asap"? If so, why was G-KSSH sitting on the ground at Duxford last week with a police belly role-pod fitted? Maybe the lease agreement to KAAT has not started yet. You have already said that, "KAAT are not expecting delivery of the aircraft for another month [or so]...". G-INFO shows that G-KSSH is still owned by PAS, so I assume that PAS are entitled to use it as they require, including using it as a police spare.
You are assuming that it will take a month to de-role/re-role the aircraft but I doubt whether this is the case. All of the "weighty gear" such as the police camera system, video recorder, ops console etc can easily be removed within a couple of days. Virtually all the electrical connections are via quick disconnect plugs and sockets.
If I was a decision maker at PAS, I would retain the internal wiring looms so that the aircraft could be used for multi-tasking in the future if necessary. Pulling a few circuit breakers would isolate the police role wiring and prevent any EMC problems. The weight and CofG penalties would be minimal.
I doubt that the Wiltshire aircraft is ever "dragged back to suit PAS...". I am sure you will find that Wiltshire Police allow PAS to use it on occasions, no doubt in exchange for some remuneration or other favour.