Upvote:5
New Orleans to Cancun is approximately 550 NM, so it would be considered an ocean passage. On a 40 to 50 ft sailboat in good conditions the trip would likely take 4 to 5 days. Source. July is early in the hurricane season, but there were no serious storms reported in that area in late Summer 1867 Wikipedia.
Looks like the greatest danger would be seasickness.