DON'T!!! use the connectors you linked to. They suck and are way too expensive. I use crimp on connectors which are low priced, and most importantly, easier to install. I realize that a crimping tool is part of the mix, but a $3 connector and a $30 crimper isn't all that much more than $13 crappy connector. Some will argue that soldered connectors are superior, and they would be wrong. The commercial communications industry has left soldered connections behind, because some, especially PL259's, are difficult to install. A lot of guys who think they do a good job on soldered PL-259's, still melt the dielectric or cold solder the braid. There is no performance degradation with a crimped on connector.
Your coax needs to be replaced too. On a C22, you are going to need 30-40 feet of coax. You don't need some big fat RG8 or LMU400 at those lengths. If closer to 30 feet, you can get away with RG58, but RG8X has about 25% less loss, but LMR240 has 50% loss that RG58 does. I use LMR240 for lengths <100' and highly recommend it for installations like yours. LMR240 costs about .70 per foot. You can find a crimper and connectors on eBay for about $30 & $3 respectively. You could end up spending close to a hundred dollars by the time you're done, but you could resell the crimper and get most of that back, or just hang on to it.
Whatever you decide, even if you go with the dreaded pinch-on connector from Catalina Direct, weatherseal it. Electrical tape will last a few months and is fine for sealing the deck connection if you regularly step the mast, but I would use something more permanent at the antenna. Hopefully I convinced you to install crimped on connectors. When you are installing that, slip three pieces of adhesive lined heat shrink tubing on the cable first. Then, after you have the beautiful crimped on connector completed, run one length of HS tubing up to the base of the connector and shrink it, then the next on top of it and then the third on top of it. This will make a durable connector that won't end up like the first pic you posted. After it's connected, weatherseal the connector. You can wrap in electrical tape, but it won't last, self amalgamating tape designed for this, or butyl tape. The butyl method is a little sticky, but probably the best seal. If you have some of the butyl tape that Maine Sail sells, wrap the connector with electrical tape first, then a single wrap of butyl, followed by another wrap of electrical tape. The first layer of tape is called a "courtesy wrap" because the butyl will leave some sticky bits in the knurled parts of teh connector. It doesn't affect performance, but will be sticky if you ever have to remove it.
Oh, I almost forgot. At the deck fitting, you can install a female connector on the cable extending through the fitting, or a bulkhead barrel that replaces the deck fitting. Sometimes, it harder to find the female connector -SO239, but you could just put a short barrel connector between two male connectors. The added loss is minimal and will not affect performance. I like the female connector on the cable - also crimped on, because the bulkhead connector is more exposed and you have to remember to seal it when disconnected.