Can you wave your notice period and take the sum tax free in your redundancy package?

No. You can't do that. If a company terminates you without notice, and you have no choice, then it might be possible, but a lot depends on history - what your employment contract says; what your employer's redundancy arrangement says; what happens to other people being made redundant, and what your employer has done in the past. Most terminations with a payment in lieu of notice are investigated in depth by HMRC.