Pathfinder – Digging with weapons

Pathfinder makes no reference to Burrow's hands. Even creatures other than a Trox can usually burrow (if they have the ability) when they are armed.

Unless GM makes its own decision, we have very limited rules for Burrowing.

First of all, on (because Pathfinder did not copy the OGL pass or create its own):

A creature with a terrier speed can tunnel into dust, but not into rock, unless otherwise specified in the descriptive text. Creatures can not charge or run while they are digging. Most creatures that dig burrows do not leave behind tunnels that other creatures can use (either because the materials they pass through are filling up, or because they do not destroy any material when digging burrows); see the individual descriptions of the creatures for more details.

Or, the Burrow trait of the Trox:

Trox has the ability to move terrier. (3 RP) They win a terrier speed of 20 feet.

Which is pretty simple.

However; the best proof is probably the Burrow spell. This is Paizo material and contains the following notes:

The use of the burrow only requires as much concentration as walking, so the subject can attack or cast spells normally. Burrowing creature can not charge or run.

This seems to imply that you have no problem keeping the spell components, weapons, or other items you need to use the ability. Spells are sometimes exceptions to the rules, but when there are no rules to exclude, they can be hints on how to handle things.

As a GM, I would question other creatures that dig burrows while armed, but additional Trox members would be sufficient justification to allow it.