What salt fly reel do you have mate?

The upper end solid bar stock type need very little care within reason.

A tighten of the drag and a good rinse in warm soapy water as you say. Don't make the mistake and blast water under pressure into the reel. Leave it to dry in a warm airy environment after and you're good to go.

I've got a range of reel sizes in solid bar stock that I have done this with for over 30 years and they are still in incredibly good condition.

A light spray of silicone over the whole thing is also beneficial if you aren't going to be using it for a while.

Just make sure you don't get that stuff over the flyline - some of the lines tend to not like some of the chemicals. I'd suggest removing the line and storing separately if you are not going to be using it for a while too.

Put up your reel model and I'm sure we can tailor make a cleaning regime for it.

Edit - all flylines need a clean occasionally. More so in the salt as they tend to collect crystals. Again, a warm wash and a run through a wet cloth/towel and some line treatment does wonders. You don't need to dress it after every trip, but you'll notice when the line starts to 'stick' for lack of a better word.