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Our party encountered a locked chest holding fragile loot. Nobody could use disable device skill, neither had the tools. Smashing the chest open wasn't possible. Carrying it out wasn't an option either.

What other alternative ways are there to open closed locks? I don't mind spells, but options that are available for mundane characters and don't require the use of spells would be the best.

What your players need to start carrying is a crowbar, the thieves go-to item of choice for forcing open a door or chest without smashing it to pieces like some thuggish Barbarian.

A crowbar grants a +2 circumstance bonus on Strength checks made to
force open a door or chest. If used in Combat, treat a crowbar as a
one-handed improvised weapon that deals bludgeoning Damage equal to
that of a club of its size.

Unlike the axe, club or sword the crowbar is an elegant weapon for a more civilized age - and doesn't involve beating the chest to a pulp in order to get it open, more the wondrous principal of the lever to pop the lid open.

If your players are feeling more flush they could buy a skeleton key:

Many door locks have a similar design and thus can be unlocked by a
similar key. A skeleton key may be tried on any standard door lock
that uses a key, even if you don’t have the Disable Device skill. You
use the key’s Disable Device bonus of +10 rather than your own total;
you cannot take 10 when using a skeleton key. The key only gets one
roll for any particular lock. If the roll fails, the key is unable to
open or close that lock. Inferior skeleton keys may only have a +5
bonus.

This allows anyone even a non-thief a chance to pick a lock.

Spells

See the Knock spell, which allows you to make a spellcaster check (with +10) against the lock's DC. Success means the lock will be disabled.

Knock opens stuck, barred, or locked doors, as well as those subject to hold portal or arcane lock. When you complete the casting of this spell, make a caster level check against the DC of the lock (see table at right) with a +10 bonus. If successful, knock opens up to two means of closure. This spell opens secret doors, as well as locked or trick-opening boxes or chests. It also loosens welds, shackles, or chains (provided they serve to hold something shut).

Mundane methods

We are in the realm of subjective GM Fiat now, we don't know the details about this chest, what material it is made of, what kind of lock (and it's material) it is made of, so it is really difficult to brainstorm a bunch of ideas and your GM could simply say "nope, that doesn't work because -reason-".

Regardless, it is commonly accepted that a strong acid, like the one from an Acid Flask, should be able to destroy a metal lock if carefully applied to it, with a bit of patience. Speaking a little about physics, a bronze lock could be corroded using Nitric acid, Hydrochloric acid could destroy tin. While iron and steel locks would take some time, but a couple of acid flasks (or the Acid Splash cantrip) should be able to destroy it.

But again, this is completely subject to GM discretion, from Destroying Objects:

Some energy types might be particularly
effective against certain objects, subject to GM discretion.

Finally, you also got the Rusting Powder, which exists to corrode metal locks:

This flaky brown powder derived from rust monster fluids causes iron and similar metals to corrode and fall apart. If you apply a dose of rusting powder to a metal lock or trap as part of using the Disable Device skill, you gain a +5 alchemical bonus to open the lock or disable the trap, but there is a 75% chance that the mechanism is destroyed and cannot be used afterward. If the check fails, the mechanism is destroyed. A destroyed lock cannot be unlocked (but still counts as locked for the purpose opening the locked object). (...)

Rusting powder is sold in a paper tube; you apply it by tearing the ends off the tube and blowing the flakes into the target device. Rusting powder does not affect gold, silver, copper, bronze, brass, or mithral, but easily affects iron, steel, and adamantine.

Knock is obvious answer, but if your arcane casters does not have it, you are stuck.

Wood Shape, on the other hand, can be always chosen by Druid. It:

enables you to form one existing piece of wood into any shape that suits your purpose.

So if chest is made of wooden planks, she can reshape plank that holds the lock and make a hole where the lock was. It won't open the lock per se, but it will make lock irrelevant.

Warp Metal may be useful too, as spell description says:

A warped door springs open

So you could use it on metal chest, or probably on metal lock on wooden chest.

Knock opens stuck, barred, or locked doors, as well as those subject to hold portal or arcane lock. When you complete the casting of this spell, make a caster level check against the DC of the lock with a +10 bonus. If successful, knock opens up to two means of closure. This spell opens secret doors, as well as locked or trick-opening boxes or chests.

The spell is sorcerer/wizard 2.