The waxed string is very easy to make. The only fiddly part is getting the oil to wax ratio right; it'll take a bit of experimentation if you're being eco-conscious and using old candles.
You will need:
bits of string, yarn, embroidery floss - I have lots of pieces of floss left over because I've just started making some hand embroidery patterns
bits of old candles
bits of old crayons, optional (I didn't use them because I save our old bits of crayon for other projects)
oil, preferably mineral because it doesn't go rancid
scissors to cut your string into manageable lengths
foil or other makeshift container for melting wax in a pan of simmering water
glossy cardboard (from most boxes of crackers, cereal, diapers; cardboard baby books also work well)
The premise is simple:
trim the bits of string to 9 inches or less
melt the wax with a little oil
add crayon bits if you want to color the wax
dip the string
lay it straight on the glossy cardboard to cool.
The trial and error comes from the various types of wax used in candles. Ultimately, you want the wax coated string to soften enough in your hands that you can shape the strings but have them hold their shape at room temperature. If you've ever gotten wax from the dentist to put on braces, you'll be familiar with the consistency you want the wax on the coated strings to be once it's cooled.
Oil lowers the melting point of wax. Pure paraffin has a high melting point. This is why spas have to add oil to paraffin for their paraffin hand/foot dips; otherwise, the molten paraffin would burn people. Pillar candles, whether paraffin or beeswax or something else, will have a high melting point because they need to be stiff and hold their shape when lit. The wax scavenged from those will need more oil than the wax from container candles, which often have added oil (and fragrance) already.
Soy wax, which is soft enough that it needs to be in a container, might not need any oil added. I had some and it worked fine on its own. The paraffin votives I found in the drawer had wicks far too short to burn, and they needed about 1 part oil to 6 parts wax. I used small amounts, though, so my estimation of the ratio might be off. I suggest you also start with small amounts of wax so you can adjust it easily. The strings don't use that much of the wax mixture, anyway.
I would've used mineral oil, but I left it at my son's preschool (I was doing a project with his class to make paper windows with spring nature scenes).
You can test the consistency after the strings cool; soy wax stiffens a bit even if it feels really sticky at skin temperature when you first dip the string. Make sure you can bend the string and shape it in your hands without any wax flaking off. The commercial wax string will leave a bit of residue on your hands, so I don't think you can completely avoid it. The wax is messiest when you first dip the string, so keep a paper towel nearby to wipe your hands. You shouldn't really need it once the strings are set and you've gotten the right wax consistency.
My embroidery floss was colored already. I could've made several colors of wax to match the color of the string, but the colors were bright enough without adding crayon. If you do add crayon, add just a little at a time; you don't need that much coloring on the string, and crayons will also stiffen the wax. The benefit of color in the wax is that it helps disguise the white areas of wax on the string where it bends without being warmed enough to soften the wax. You can still see this on the commercial wax sticks; if you bend them without warming them in your hands, they'll get pale and look almost crumbly at the joints (but the wax isn't stiff enough at room temperature to crumble off in chunks).
What do you do with them?
Make pictures. You can stick them on whiteboards, glossy cardboard (like you should've used to set the strings on to cool), or even metal sheet pans and windows. The wax sticks, whether commercial or homemade, will leave a bit of waxy residue on glass, but it's easy to wipe off. Some commercial sticks suggest making a lot of 3d projects, but those are usually a pain to matter what brand you use. Your hands have to be warm or the waxed string won't stick to itself. The projects still pull easily apart, which is why they advertise that you can reuse them "over and over again."
If you have baby books with letters or shapes, you can show your kids how to outline them with the waxed string. It's a great tactile activity for getting them more familiar with shapes. Small whiteboards with a cardboard backing are usually cheap, and make a great base for the wax string if your kids need a quiet activity.
I have sensory kids and they're not very skilled at sticking the strings down securely in order to make detailed pictures, but they like to line them up, twist them together, drop them in a pile, and stick them to the window. They also like watching me or another adult make pictures or trace shapes in books with the string.