Replacement for cyclohexane
Cyclohexane is used for this extraction because it is nonpolar, as is iodine. A more polar solvent like acetone or ethanol will also extract a whole bunch of other stuff like essential oils, proteins, and other polar compounds.

You want Mineral Spirits which you should be able to purchase at any quality hardware store or Walmart. Mineral spirits, mineral turpenine, or whatever you want to call it, is a mixture of saturated hydrocarbons distilled from petroleum. It is a general purpose paint thinner for oil-based paints. Since it is mainly C7-C12 alkanes, it will have a higher boiling point than cyclohexane $(140\ ^\circ\mathrm{C}$ vs $81\ ^\circ\mathrm{C})$., but it will have the same general polarity as cyclohexane.

If you can find products labeled as petroluem ether, light naphtha, or ligroin, all are alkane mixtures with lower boiling points than mineral spirits.

Another common low polarity paint thinner is toluene, which has a lower boiling point at $110\ ^\circ\mathrm{C}$.