Interrupts should easily detect 4uSec pulses and that's probably the only way to detect such short pulses. Go slowly. Interrupt code is very difficult to debug. Keep the interrupt service routine (ISR) as short as possible - 2 or 3 lines of code if at all possible.
Why do you want to replace polling "with a proper hardware timer". That sounds like polling isn't respectable. Polling is a perfectly good way to collect data. Why make things difficult for yourself.
It would be very helpful to your cause if you give us a description of your project, including the hardware you are using.
...R