Thanks for the comments
Yes, I fixed the handguard wobble using tape:
The buttstock wobble was a bit harder to sort out, but I ended up using a special kind of glue that expands as it dries. The stock didn't wobble just as much after I applied the glue, but it was still noticeable, so I decided to add some tape too. This almost sorted the problem out. I ended up tightening the screws that hold the stock in place. Now the stock feels pretty solid, but there is still some movement.
A combination of glue, tape and some tightening pretty much fixed it