Implement IR protocol using only one timer
I have a simple non-preemptive RTOS that uses only one hardware timer, so: YES, of course you can do that with one timer.

Just configure that one timer to keep track of time, and you can at appropriate points in your software wait until the proper time has arrived to do the next thing. 

A minor inconvenience can arise when your timer rolls over, but assuming you inspect the timer often enough you can maintain an extension of the timer and increment this extension whenever the current timer value is lower than the previous one.