Slocum got his longitude via the moon. It was a relatively time consuming method of getting a fix that was superceded by longitude via accurate time pieces. By the early 1900s it had fallen almost completely out of use and the tables were removed from Bowditch. Chronometers capable of keeping time accurately enough for navigation were still relatively expensive when Slocum sailed and beyond his budget.

Almost any quartz watch is more than accurate enough for navigation. A couple of Timex's would be fine. Personally, have a solar powered Casio Pathfinder digital watch. It has the distinct advantage of having a dial large enough for me to see without glasses.