If you want to eliminate the spawner, all you want to do is hit it by using a pick
axe. This will kill the spawner.
In case you do not believe that they will manage to defeat the newly created
spawns, you can just steal from the chests by prospecting your path around the
sides of the location and through the walls. The monsters will not be able to reach
you in a single block hole, but you will have the ability to grabbing the loot from
the chests.
If you want to test your fortune, you can easily eradicate the chests and run
through the area while grabbing the treasure and running back out. Smashing a
treasure chest can cause all the items inside it to fall on to the ground, so if you
have sufficient inventory space this could work flawlessly.