How can I safely open the chest in a Wood Wall Trap?

There are a couple of ways to deal with the fire trapped chest:

First you can disarm it by grabbing the gun powder out of the chest first. If you take that item out of the chest the trap will no longer trigger. You have to do this pretty quickly for it to be effective.

Second is prevention. The chest is what catches fire. You can prevent it from spreading. Hammer away the nearby wood walls so that they don't catch fire when the trap triggers. You can leave most of them standing, just hammer the ones that are nearest to the chest so the fire can't jump to them. You can always rebuild them later after the fire stops burning.

I opened it safely by just storing some rocks in the chest. I was able to grab everything out of it then.