Can I use IIR or FIR to get a sliding mean?
It corresponds to an exponentially weighted moving average (EWMA) filter with parameter $\alpha = 0.01$.

The difference equation can be expressed as:

$$y(n)-(1-\alpha)y(n-1)=\alpha x(n)$$
$$y(n)-0.99y(n-1)=0.01 x(n)$$

Thus it's an IIR filter. You can easily get the coefficients from the difference equation.

$$Y(z)-0.99z^{-1}Y(z)=0.01X(z)$$
$$\frac{Y(z)}{X(z)}=\frac{0.01}{1-0.99z^{-1}}$$

Therefore, a = [1 ; -0.99] and b = 0.01.