Although WD40 is touted as a super lubricant it isn't actually a very good lubricant. It's best use is to quickly and temporarily loosen something so that the "stuck" part can be pulled out and properly cleaned and lubricated with a "real" lubricant. It does not leave all that much "lubricant" behind when it evaporates, so the stickiness is likely to return fairly quickly unless something else is used once the sticky parts can be moved enough to spread "whatever" less penetrating real lubricant you use after the WD40.

WD40 penetrates small cracks quite well. The ability to penetrate where it shouldn't be was the reason the US Army banned it's use in Korea and Vietnam since it wicked into and destroyed the primers in ammunition if used on the gun. (The guns worked fine, but didn't go bang.) The ability to displace water makes it great for "drying" a wet ignition system so you can restart your car after it's been for a swim, but nearly any other use requires a follow up to "finish the job."

A children's accordion is likely to have mostly plastic parts that won't be harmed by plain water, or water with a small amount of soap; although there may also be wood and/or felt/cloth parts that shouldn't be soaked. If the stickiness is due to the keys rubbing against each other, it may be able to pull the edge of a dampened cloth through the cracks to get some of the sugar from the glazed donuts out, or a thin "blotting paper" used edgewise might work to clear the cracks.

If the problem is in the "linkages" inside, the best cleaning methods (and especially the materials to use) would depend on the details of the design.

Plastic parts are somewhat prone to "warping" and an old instrument might have keys or other parts that rub and stick just because they've changed their shape. It the "rub" point is clean, sometimes a scant puff of graphite (the kind used in locks) will provide enough lubrication to be helpful, although any excess can leave a "stain" on your fingers and clothes. If you can find where the sticky is, a dab of petroleum jelly (petrolatum?) is a fairly decent lubricant for cases of friction binding. (I've even use Mentholatum for lots of such "fixes," and it works pretty well if you like the smell.)

John