AHi,

I'm making a cake for a child's birthday and I don't want to use alcohol/vodka to make the powder into liquid for obvious reasons!

is there anything else I can use to mix with the powders like extracts of some sort ... any suggestions would be a great help!?

lemon extract

AAlthough the vodka evaporates completely leaving no alcohol on your finished product. It's only there to dissolve the powder to allow you to paint with it. Don't stress, there's no issue using it on children's cakes.

All extracts contain alcohol, and alcohol is alcohol, so there's no real difference there.  The difference is that extracts also [often] contain oils and those oils help to keep the paint fluid and extend working time.  Alcohol evaporates once exposed to air, so really, it's a non-issue.

You can make "paint" using powdered colors by mixing them with vegetable oil [makes a nice "watercolor" type paint.  Doesn't completely dry, so you need to be careful].  You can also mix them with vegetable shortening and get an opaque paint.