Experimentally it appears that the modulus of the Hankel function of the first kind, $M_\nu(x)$, monotonically decreases for $\nu\geq 0$ and $x>0$. Here is a plot of the first 12 Hankel functions of first kind illustrating that they are monotonically decreasing.
It seems that this should be possible to show with the formulas at https://dlmf.nist.gov/10.18 (for example showing that $M_\nu'(x) < 0$)