Do I need a dogbone or egg insulator at each end of my dipole, or can
I just splice the antenna wire to the nylon braid that runs to my
trees?

If you use insulated wire for the antenna, just tie the nylon to the wire.
Anymore, insulated wire is all I use for my antennas cause Home Depot doesn't
sell bare wire small enough. I prefer #18-#20 insulated and stranded (not
avail. at HD either). They do have #14.
73 Gary N4AST