Can I put a 250 mA fuse in replacement of a 160 mA fuse?
Widening of protective envelope for any circuit is NOT good. the fuse is there to protect the circuit in case of overcurrent. Overcurrent does not mean shortcircuit, it means that the circuit is design at certain current level, in your case according to original fuse is 160mA. everything above that is overcurrent event and a fuse must deal with it to protect the rest of the circuit. even tough it seems like not a large current 250mA in respect to 160mA is increase of 56,2%. It is like driving 95 in 60 km/h zone. just put this in perspective and you will see that even though you can use any fuse to make the circuit work only the one specified for this circuit will be proper.