You can't just throw in a bigger breaker, and expect it to work the way you want.
First of all, you're going to have to have the utility install conductors sized appropriately for 200 ampere service. Depending on how the building is wired, you'll also have to upgrade the conductors that run from the service drop to the meter (this might be handled by the utility, depending on how the building is wired). Next, you're going to have to upgrade the conductors that run between the meter and the disconnect (likely handled by installing the new panel pictured). Finally, you may have to upgrade some of your grounding and bonding conductors, as they are typically sized based on the size of the service.
Once all that's done, then you can likely proceed as you've described. However, you're going to have to evaluate how the system is grounded. The service neutral will have to be bonded in the new panel, where the 200 amp disconnect lives. Then you'll have to feed the existing panel (now a secondary panel), with a 4 wire feeder (hot, hot, neutral, ground). You'll also have to isolate the grounded (neutral) bar in the existing panel, if it's not already.
Long story short, this is not a simple job. There are a lot of subtle details, that can easily be missed by a DIYer. I would recommend having an Electrician at least help you plan the project, and inspect the completed work.
You'll have to use a cable or wires that are rated for wet locations. You'll most likely use Underground Feeder (Type UF) cable, Underground Service-entrance cable (Type USE) , or THWN wires.
You'll have to install a proper grounding electrode at the cabin, and bond the grounding conductor to it.
You'll have a grounding electrode at the pole, where you'll bond the service neutral and the equipment grounding conductor. From there you'll run four wires (two "hots", one neutral, and one ground), and you'll keep the ground and neutral separate.
Best Answer
The 200 A capacity of the meter base and/or panel is the max capacity of that panel. If you put a 100 A breaker to protect it, that will be fine. You only create a safety concern if you put a breaker that has a GREATER capacity than the equipment it's going into.
For example you would NOT put a 200 A breaker in a 100 A panel.