Couldn't you just surreptitiously swap the seeds for known, 'quality'
cultivar seeds?

Doesn't quite work that way -- apples have some interesting genetic
instabilities that make even grafting known cultivars less than a sure bet.
And seed of any open pollinated, sexually reproduced seed (as opposed to
apomictically produced seeds, as dandelions often do) is going to produce
offspring different from their parents. (Just like human kids, while they
resemble their parents, aren't exact duplicates. And one sibling is not
identical to another.)

It's only with some fairly intensive breeding techniques (e.g. linebreeding,
back-crosses) that we've been able to produce the uniform fields of
plants currently in favor with mechanized agriculture.

John Chapman certainly wasn't toting around bags of grafted apple trees when
he decided to spread apple seeds around on his journeys. Some of the
seedlings that came up produced very nice apples. Some didn't. It's the
same result I'd expect of the OP's little experiment... they may get
some nicely flavored apples from the seedlings, and then again, they
might get spitters. But whatever they get, it'll be interesting for the
kids if the parents help them interpret what they're seeing and
experiencing.

someone earlier claimed that the OP would get "crab apples" from the
seedlings... this is pretty unlikely, as most of the eating apples are
diploids, and most of the crabapples are polyploid (have several sets
of chromosomes, rather than simple pairs.)

At any rate, I think kids (and grownups, too, from the sounds of things
here!) should try things like growing seeds of an open-pollinated, sexually
reproducing crop, just to see some of the hidden genetic variation
uncovered... it's really pretty amazing. I also wish I could get more
people involved in such activities as comparison tastings of fruits --
or as my husband said after I got him to try about 50 cultivars of apple
in a day, "Gee, I wish I'd known before now that there were more apples
than Delicious and Jonathan." (He has now found he also likes tomatoes,
pears, sweet corn and I'm working on getting him off iceberg lettuce. g)

Save some seed of something or other... tomatoes, dwarf marigolds,
impatiens, lettuce... grow 'em out and see what you get. It's fun.

Kay