The best starting point to use is a simple 1:1 substitution.
You can use different liquids to make a custard; a zabayon, for example, is a custard made completely with fruit juice. Dairy is not the defining component of a custard.
There will be differences in texture when you do it that way. The custard itself already will act differently - the acid itself will influence the custard and its thickening, especially if you add the chamoy before cooking the custard. If you add it afterwards, I expect less curdling, but the base itself will now be more liquid. And overall, you will have different ratios of liquid to fat to nonfat solids, but also some pectins from the fruit-based sauce.
Even though you cannot predict the exact effects and a "perfect" ratio, the overall effect won't be clearly in a direction where you know you should make adjustments. You will need a starting point before starting to tweak, and in the case you have, 1:1 is good enough for that, and it is also the best guess you can make. And with the tiny amounts you are planning to use (which surprise me a bit - did you only want to use an additional note of the flavor?), you may not even notice much of a difference.
Even if you start using more, you will still likely have to go for 1:1 with the total liquid amount, but add enough sugar to the chamoy (before measuring it for the 1:1 substitution) to prevent crystalization. Or just use a recipe for a good custard-based fruit ice cream, and instead of the fruit puree, add your chamoy. Or, if that is too intense for you, substitute some part of the fruit puree for the chamoy, again 1:1.