Ken, or Christine (probably not Useless) - you bring up an excellent question. I'm going to give you my opinion, and others may have different ones. Choose the one you like the most.
Your trailer is 22 ft long, but the living space is less due to the way HiLo measures trailers. I think the "box" is about 19 ft long. (You could measure this if you want). The width of your trailer is about 8 ft. The interior dimensions of both length and width will be somewhat less, but let's use 19x8 as a conservative estimate of the area you need to cool. That area would be 152 sq ft.
Now, I have a portable air conditioner in the guest room of my home which is an A-Frame and is on the third floor. It is about 360 sq ft and the "walls" are the roof. Like most A-Frames, the only insulation is the roof shingles. The air conditioner is rated at 11,000 BTU/hr. It keeps the room comfortable.
Your trailer has less than half the area to cool and has slightly better insulation. I assume it is also painted white, which should help immensely. As a result of this comparison analysis, I'm of the opinion that a 9200 BTU unit would cool your trailer just fine. It would run more often/longer than the old one and would probably take somewhat longer to cool the interior down if it was starting from a hot condition, but those are minor concerns. Running more often, it might even feel more "comfortable", because it would dehumidify the air more constantly than the old one.
The only real issues would be the mounting on to your trailer and water drainage. It probably won't exactly fit the old opening, so you may have to make some adjustments there. AND, you will have to be very careful to duct the water it condenses from the atmosphere away from the interior, or you will have the "interior rainstorm" that has been posted here recently.
Other than those considerations, I think you have a good idea and look forward to seeing the results of your "mod". It should be more efficient and "quieter" than the old one too.
- Jack