PWM is controlled by a logic circuit which is usually controllable.
However if you have no access to the logic controller, you can easily generate your own from a cheap Picaxe chip, provided your circuit uses 5 volts and can be driven with less than 20 mA.
Google Picaxe for details. These are simple computers on one chip with enough memory for simple jobs and an interesting toolkit of tricks they can do. Chips suitable for this can cost less than $5. Programming is in a Basic-like language but with a lot of I/O commands. The programming editor is free and a programmer can be added to your circuit board with 2 resistors and a socket.
Another way would be to trigger a monostable on the rising edge of the incoming PWM then vary the length of the output pulse with the monostable and retrigger on the next rising edge. Since this ignores the falling edge of the incoming waveform, you have complete control of the PWM.