Perhaps someone from Aerotech can chime in, but I successfully drilled an F40-4W down to less than a second delay from burnout - story here:
https://www.oldrocketforum.com/showthread.php?t=18716
In short, staged a composite F40W to a BP F15-6 on an Estes Mammoth, using the F40W ejection charge to light the F15. Worked like a charm. My intent was for the ejection charge to fire less than a second after burnout - which is just what happened.

My concern with doing that AP to AP is that AP is far harder to ignite than BP - I don't think 4F black powder will reliably ignite AP. Perhaps if some small bits of AP propellant were added to the BP ejection charge?
I'd certainly do some ground testing before I tried flying it...