It is difficult to find a single verb translating shuffle, randomiser is ugly, réorganiser de manière aléatoire l’ordre des images is technically correct but too verbose¹ so, assuming the space allowed to the caption is sparse, the best choice is mélanger les images.

There is also the verb battre which is common with cards (battre les cartes / shuffle the cards) but it doesn’t work with images.

¹_{Tri aléatoire has rightly been suggested. It might look an oxymoron but the images can actually be “randomly sorted” by a program, for example according to a randomly chosen key.}

1.As I think that button captions do not necessarily have to be very concise,

2.as I believe that sometimes they are not and

3.as I’d rather have as much information as possible in a caption, specially considering the emptiness of the screen around a multitude of captions that are brief but at times quite opaque,

I wouldn’t mind reading your caption as

“nouvel ordre aléatoire“

or even

“nouvel ordre aléatoire

des images“.

If the button is below a set of images, I don’t think that it is necessary to mention image in the caption.

I therefore suggest to focus on the action, which then depends on what you do exactly with your images:

If you keep the same set of images but modify their order on the screen, I would use

ordre/mélange aléatoire

e.g. images 1,2,3,4,5 –> 5,2,3,4,1

If you have more image than the number of images shown, I would use

tirage aléatoire

or, because “tirage” is often random (e.g. le tirage de la loterie),

nouveau tirage

e.g. images 10,25,1,99,12 –> 88,24,6,35,5

If you like to mention images on the button, you could use:

mélanger les images

in the first case (reordering) and

tirer des nouvelles images

in the second case (random sampling)

If you want to keep it concise:

• Images au hasard
• Images aléatoires

I think it is best to avoid the verb here for concision.