Hey Froggy! I'm no expert and I believe every plant responds differently, so take this with a grain of salt...
I have a different feeling about this. If you didn't have such a healthy plant right next to it, I would say leave it alone and hope for the best. However, because the other shoot is doing so great, I would cut and remove the unhealthy one. This is why:
It is common practice to prune plants of unhealthy growth. The reason is two fold. One, because the unhealthy/damaged growth
may be the result of disease or infection and you don't want it to spread. And two, because the plant can put its energy into the healthy shoot, instead of trying to sustain something that will succumb anyway or remain stunted.
Keep in mind, I don't have alba. But I do have viridis and it is always putting up more shoots. If I had one looking bad, I wouldn't hesitate removing it, knowing more are to come.
Just my two cents
Also, please note I can't see enough detail in the pic to provide an opinion on why the one shoot is suffering. Although it kinda looks like it might just be mechanical trauma (perhaps from shipping?)