Did Aragorn really walk around the Wild with just a broken sword for protection?

[Groin Redbeard]

Isildur took the shards home with him. Shortly before Isildur was killed in the second year of the Third Age in the disaster at the Gladden Fields, the shards of Narsil were rescued by Ohtar, squire of Isildur. He took them to Imladris, where Isildur's youngest son Valandil was fostered.

The Shards of Narsil became one of the heirlooms of the Kings of Arnor, and after the Northern Kingdom was destroyed they remained an heirloom of the Rangers of the North. The sword was reforged in Rivendell in 3019 T.A. during the War of the Ring, in celebration of the rediscovery and capture of the Ring with which it had become associated as its symbolic antithesis.

Now it is my opinion that Aragorn would take this on his trips through the wild, maybe not the shards, but at least the hilt. This would serve as a reminder to him of his ancestory and an inspiration to his fellow rangers. Narsil certainly wasn't his primary weapon of course, I'm sure he carried another sword. It would serve as a proof of his heritage not only to himself but to those who met him. He could very easily prove who he was by the shards on him.