I hate to keep being the naysayer, but I'd strongly recommend against dielectric grease inside the connector. Several years ago, I put a layer of it on the SO-239 of my TM-D700 just below the threads so the connector would screw on then reach the grease at the end to seal the entrance. The radio is installed under the back seat of my truck. After about 3 years, I was having a lot of TX/RX problems (which first cropped up while supporting a bike race).
Upon investigation, I discovered that the grease had worked its way up the threads and had eaten away at the connector. Some locking teeth were dissolved. There was green copper oxides bunched up around the center pin inside the radio. The connector was totally toast. I ended up having to replace the connector on the radio and scrapping the end of the cable. I'm sworn off dielectric grease for RF use forever.
Another reason not to put it up inside the connector is that it is intended as an insulating protectant. Its purpose is to coat connections externally to retard oxidation. Exactly why it was incompatible with the plating (and base metal) on the Kenwood's factory connector, I don't know. I've never seen it eat anything else before. I suspect the RF played a role though.
And now you know the underlying reason I don't think that *anything* gooping up inside an RF connector is a good idea.
YMMV
I endorse Jupiter's other recommendations though. Good advice there.
ETA: On closer examination, I don't think Jupiter meant to pack the grease inside the connector, but that wasn't really clear on the initial read. Still, I won't get it anywhere near my RF connectors.