Since I will be charging the negative voltage capacitors again by the capacitor's negative terminal, I don't know if I should charge those polarized capacitors by the negative terminal.
I'm not sure what this means. Charging a capacitor by a single terminal is nonsensical, it's a two terminal device and current flows through it according to I = C dV/dt, which applies to both terminals.
You can use polarized capacitors if the voltage across the capacitors stays equal or greater than 0V. It's difficult to tell from the plots (and unfortunately CircuitLab doesn't seem to know how to plot the voltage across a component, which is silly), but after playing around with the simulation, it looks like this criteria is met and you could indeed use polarized capacitors.
It's worth pointing out that using polarized electrolytics for this: ceramics will likely outperform electrolytics in numerous specs at this capacitance/voltage, so you might as well use ceramics. Almost certainly smaller, for one.
Edit: after a quick look at Digikey, if you're using SMT components, you're almost forced to use ceramic. There are loads of 1206 1uF ceramics, very few SMT aluminum 1uF caps with a voltage rating above 100V.