Replacing push button by transistor in 555 circuit
In your solution, current flows the same direction in both transistors.  You need a bi-directional conductor of some kind because current flows either into or out of C1 depending on the state of the latch.

One option is a small reed relay; not sexy, but it works, and C1 debounces the contacts.  Another is one section of a CD4066 CMOS analog switch.