Hi,
I've tried several things. Now I pretty much always start with a tight wrap of two layers of thin masking tape, then cut with a Dremel, using the larger, reinforced cutoff wheel. Leaving the masking tape in place, I always blow some compressed air through the freshly cut hose, to make sure no particles from the cutting are left inside.
It helps to leave one layer of the masking tape in on the hose while installing the collar. Some collars are a very, very tight fit, although larger hoses like AN10 or AN12 you are likely using for an oil cooler are often easier than smaller sizes.
It can also help push the collar onto the hose by seating it backwards in a deep well socket. This gives you something to grip or even tap with a rubber or plastic mallet, if necessary.
After the collar is started on about half way and with all the loose S/S wire ends now inside, I peel off the remaining layer of masking tape. Then press the collar the rest of the way on, until the hose is fully in contact with the ridge around the inside.
Now it's time to put the end on. Clamp the collar in a vise, and put a few drops of motor oil on the end. Start the end and tighten until it's fully against the collar.
That thermostat is a good idea to keep the oil from flowing through the cooler until after it's partially warmed up.
Very Important! Always wear eye protection when cutting that hose! It's common for little pieces of stainless steel wire to go flying and they could do serious damage to eyes!
Cheers!
Alan