The Wand of Fireballs (as well as several other magic items that have charges¹) has a chance of the item being lost forever when the last charge is expended:

If you expend the wand's last charge, roll a d20. On a 1, the wand crumbles into ashes and is destroyed.

I am looking for ways to influence this roll to lower (or remove completely) the chance that the wand will be destroyed. Unfortunately, so far I have been unsuccessful (barring the usual "Wish can do anything").

Things like Inspiration, the Divination Wizard's Portent and the Lucky feat all specificy which rolls they apply to so can't help with this particular d20 roll.

Are there any class features/abilities/spells/anything at all that are able to influence this d20 roll to avoid the destruction of the wand of fireballs?

Any official source will do, including UA as well.

^{1. Asking specifically for the wand of fireballs to avoid possible magic items that work differently, making this too broad}

There (probably) isn't

The wand destruction check is a flat d20 roll with no particular name or mechanic. AFAIK, all the features that interact with a d20 roll are limited to, at least, "attack roll, ability check or saving throw", e.g., Halfling's Lucky and Wizard's Portent.

Lucky: When you roll a 1 on the d20 for an attack roll, ability check, or saving throw, you can reroll the die and must use the new roll.

Portent: [...] You can replace any attack roll, saving throw, or ability check [...]

Interacting with the Wand roll would require a feature that allows you to modify/interact with any d20 roll, which does not exist, at least from my knowledge (couldn't remember any or find any on PHB, XGtE and DMG, which are the most likely books to contain something like this).

Side note: I am inclined to say that, even if there is such a feature in UA (which I personally doubt, but anyway), it is likely that it would be due to lack of refining in the wording, and not actually intended.

Therefore, the best way to not roll a 1 in this d20 is simply not rolling the d20 :P (i.e. not spending the last charge)

There is no feature, spell, etc that can do what you want. The only way to ensure that the wand doesn't destroy itself is to never use the last charge.

Probably not

There are a few ways to change a d20 roll (a School of Divination Wizard's "Portent" feature, a Wild Magic Sorcerer's "Bend Luck" feature, a Halflings "Lucky" attribute, or even inspiration); however, they all say:

...whenever you make an attack roll, an ability check, or a saving throw...

The writers' consistent specificity indicates that they did not want rolls like you are asking about to be affected by class features/abilities/spells/anything at all.