Perhaps connect the reed switch between two PIC pins.
One output pin driven low when sampling the switch, the
other as input (with interal pullup enabled) to read the
switch. That way, the curcuit will only draw current when
the output port is driven low (even if the switch is
closed for a longer time).

That is, if the impedance of the internal pullup is
enugh to filter out the cable noice.

Jan-Erik.

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