I'm not posting much anymore regarding LP12 useage since the truth doesn't seem to matter much to Linn's detractors. I'm making an exception this time because I hate to see an honest question answered incorrectly. This is not an insult to any of the above posts as each has individual merit. My take on this is based on Linn LP12 ownership for nearly 30 years. The detractors are welcome to fire away. My shoulders may not be as muscular as they once were but they are still wide and can take it.
It's doubtful that the vibrations you are experiencing from your current wall mount shelf are reaching the stylus in the groove IF the table is adjusted correctly. The LP12 is a suspended table which by design decouples the record/cartridge combinations from vibrations down to around 8 cycles. If the suspension is out of adjustment, you are using a non-felt mat or any other tweak that couples the suspension/record like a clamp then you have altered the tables operating parameters to possible sonic degradation. I believe the Neuance shelf to be a reasonable upgrade.
Assuming your table is mounted on a shelf directly centered between your speakers and on a load bearing wall, low frequency vibrations of a sort that would reach the groove would need to come from heavy traffic of some type outside your home. Rear ported speakers or a subwoofer placed nearby are a real concern however, IMO. One way to check this out is to take the grill covers off your speakers, play a record and take note if there is any pumping of the woofers during play. If not, you're okay as is but I still support the use of the Neuance, but that's about the extent I'd go with. Please, trust your ears.
I know from experience that a high mass stand will work just fine with an LP12 on it so I'm not opposed to that method at all. In a practical sense though placing enough load from a rack onto a rickety floor to eliminate the bounce is a guessing game at best. Again, the biggest problems for the Linn are footfalls and rear ported speakers.
I've archived a number of setup and tweaking tips on the LP12 found online through the years. Email me direct if you would like me to forward them to you.