There isn't much need to disinfect nets if they go from salt to fresh. But I would rinse them out under the tap before moving them from fresh to salt. That is because there are more diseases in most freshwater tanks than in saltwater tanks. And although most diseases won't survive the transfer from fresh to salt or back again, I am paranoid about TB, which might be able to survive.
The other option is to dry them out before using them.
In the shop we had a bucket of fresh water and a bucket of salt water. Any nets that got used in freshwater were then put into the saltwater bucket. Likewise any nets that were used in saltwater tanks were then put into the freshwater bucket. The buckets also had a double dose of broad-spectrum medication in. The buckets were tipped out and changed each day.
At night we would take the nets out, rinse them down with fresh water, and allow them to dry overnight.
In the quarantine room we would have one net per tank, and if they were going to be used on another tank, they were soaked in a mild bleach solution for 10minutes or so before being rinsed off with freshwater.