You are not saying a thing about the signal, or the system,
that would drive selection.
You can get relays in the same form factor as a packaged IC
(at least DIP-scale).
A relay will be more resilient to many faults, will default to
an open condition with power off, and does not require
that your control and signal have any common connection.
An IC mux may, or not, provide specific fault protection.
Some offer power-off high impedance as a special feature.
All constrain the input signal to be within the supply rails
for normal operation (low impedance on condition). An
IC mux will almost certainly have lower supply current
demand than a normal relay, more than a latching relay
if the toggle rate is low.