Adding a remote switch and battery to a 9 volt dispenser
Sounds like a fairly marginal design. A fresh alkaline 9V cell has an internal resistance of around 1.5-2\$\Omega\$. Cat5 is supposed to be AWG24 so a 40' loop should be around 1 \$\Omega\$. 

If you parallel 4+4 as Roger C suggested in a comment that will be reduced to 0.25 \$\Omega\$. If you can measure a resistance that low then you can check it. 

It's also possible the circuit would be happier with a cap like 1000uF/10V across the supply at the device end, but that would be more of a transient issue with the timer circuitry. Suggest you do both.