If you want your new cable and antenna to last, you need to listen to buddrousa. Water will find a way in. That water will cause corrosion that will run down the copper in your new coaxial cable and destroy it in short order. All the labor you spent putting it in will be wasted. You'll need to replace the entire cable.
Industry standards are to wrap the entire connection with a layer of electrical tape to ease disassembly later.
Follow that up with a layer of butyl tape molded in around all the connections.
Put another layer of electrical tape over all that to protect it from ultraviolet light.
The heat shrink tape is a nice addition and helps with strain relief, but it's not a replacement for proper waterproofing.
There are a lot of people that do not properly waterproof their connections and "get away with it" for a certain amount of time, however, that shouldn't be taken as a reason to not properly waterproof your own connections.