Matched filter for "amplitude SNR" vs power SNR
Power is proportional to the square of amplitude, so there's really no difference (since SNR is always a positive number) when maximizing: A filter that maximizes "amplitude SNR" maximizes "power SNR".

So, if your application requires you to maximize the amplitude ratio between signal and noise (be careful, amplitudes can be negative or complex, depending on how you define them!), then that's the same as requiring you to maximize the power ratio.

I.e. 

$$h_\text{opt} = \arg\max_h E\left\{\left(h^H (vv^H)h\right)^{\frac12}\right\} = \arg\max_h E\left\{h^H (vv^H)h\right\} $$

since the quadratic form $h^H (vv^H)h$ (which is the power of $y$) can never be negative, and that makes your square root both unambiguously invertible and monotonous.