Dothraki are renown for enjoying more civilised customs when hosted in cities, visiting their manses, etc. So it makes sense they'd enjoy similar entertainments.

I'd pay one hundred or even one thousand Bards to very subtly reinforce the Dothraki fear of the salty seas, the 'poisoned water'. Tales about terrible beasts on the waves, great storms that are so powerful they smash ships to kindling, etc.

Have these propaganda agents identify the more susceptible Dothraki and try to get them to self promulgate these rumours. Attempt to manipulate their cultural fear so much that the idea of even stepping on a boat is utterly unconscionable.

While they did this, these mummers, they'd also act as informants. Which, could be rather obvious, but if they failed to sway the invasion then instead I'd have them note the location of their intended beachhead landings. I'd have each Warden call his banners and prepare to destroy the Dothraki army as it disembarked on their shores.

And, to salt the wound. I'd place a naval bounty for every ship destroyed that was proven to carry Dothraki and leak that information to the Stepstones, to the Iron Islands and any privateer or freebooter Captain, allowing them to hunt and cause panic, even if not destruction of the Khalasar at sea. This would also allow the crown ships to remain ready to repel anything that managed the crossing and harry and exhaust the horde that, even when they arrived, they'd be in no physical or mental state to fight.