*What is the injury risk*
To establish what the concern is: 1) the next joint up is the elbow* and that is the one that will have extra stress 2) "joints" tends to either mean tendons or ligaments. I doubt there are any studies on Beat Saber, but this is similar to tennis. In tennis you hold an object of ~1lb at the end of your arms; plus when you hit the ball there is much more force than just weight of the racket. I expect any injury from the weights would be similar to tennis elbow, which is inflammation of the tendon in the elbow.
I wouldn't expect this to be a big deal at all. 1) Most people over 40 have scar tissue in their tendons, most people are basically unaffected by it 2) Not everyone in tennis gets tennis elbow 3) Because there is a more consistent force rather than the sudden impact of the ball I expect this to have a lower injury rate than tennis (note how pulling the slack out of a barbell before lifting it drastically improves safety when the movement is less sudden)
*Yes the shoulder is a thing, but based on watching a single video of Beat Saber on youtube I don't expect much additional shoulder stress from the weights
*Should you use them while playing*
Eh, I'd base that more around what's fun for you. If ya wanna get ripped, you'll need more than this. If you wanna get skinny, that's mostly in the kitchen. If ya wanna improve your cardiovascular health this will help but I don't expect the wrist weights to make or break it.