Could we talk you into replacing the whole circuit with an Arduino ? smiley-evil
Forget the diodes and put another buffer between the base trigger and the input circuit.
If you need that manual trigger then turn that buffer into a logic gate. The type will depend on the normal state of the output of the 74LS93. If it is normally low then an OR gate should do. You should connect the input of the OR gate through a potential divider to get a safe input level to the gate. You should not feed over the supply voltage into a gate.
I am sorry but got lost here, what OR gate?
I really don't know what is the normal state of the 74LS93 counter is, the 555 timer is always running.