I am guessing that (1) you don't have LM158 or LM2904, which are in the same family, otherwise you'd consider trying them; and (2) you want to use a dual with the same pinout so that you don't have to adjust the strip board layout. If you are planning to use a socket for that IC, you can of course just try some other duals in there (what do you have? TL062/072/082? LF412? NE5532?) if they have the same pinout, and see how it goes.
The LM358 is not particularly fast, but it IS single-supply. If that circuit depends on that characteristic, your pickings will be slim. I haven't scrutinized the oscillator in the schematic yet so I can't say, but if it isn't oscillating all the way to the rails (GND and +9V) then another dual may serve just as well.
In this discussion,
https://tagboardeffects.blogspot.com/2019/09/keeley-magnetic-echo.html,
it seems that others have gotten it to work using TL072 and TL082. The TL072 (and TL082, I think) is known to have problems if the input is driven too close to the negative rail (GND in this schematic), so I would guess that if TL072 and TL082 work in this circuit the specification of LM358 is not because it is single-supply, but because it is cheap and good enough.