[See the circuit below]
Forget pulsing, just set the pin HIGH and leave it high.
The relay will latch because of the current flowing through C1 as it charges. Once it's fully charged current flow will stop, but the relay will remain latched. The most important bit though, is that C1 is now charged up to the positive voltage you applied.
When you're ready to unlatch just pull the pin back low.
Now the positive end of C1 is grounded, which means the relay coil will get a negative pulse as the capacitor discharges.
Now, as a disclaimer, I don't know how robust a PIC (or other microcontroller is), but an ATTINY/ATMEGA can handle it. I set one up to latch / unlatch 100 times per second and left it running for several days.
If you need to control multiple relays from the same microcontroller you'll want a push-pull amplifier to take the load off the microcontroller, but for a single relay all you need is a capacitor.
View attachment 27835