Can I use electrolytic capacitor in a schmidt trigger oscillator
You can use two 22uF capacitors in series (back to back). Or bulky and expensive film capacitors. Or unpolarized electrolytics,

Or use 100V 10uF aluminum electrolytics and hope for the best. Polarity does not matter since it reverses, higher voltage caps can tolerate some reverse voltage. They won't explode if insufficiently rated, your circuit just won't work.    

But really, now, this is 2015 and nice X5R 10V 10uF 0805 capacitors cost something like 15 cents in small quantity.