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If the switch has no grounding screw and the box is plastic, there is no need to connect the ground wire since it just isn't possible in your situation.
You do not need to cap ground wires, since most times they are bare to start with, unless yours is insulated and in which case you would cap it off.
Just push it back in the box so that it cannot touch any of the power connections and it will be safe and fine.
Might think of getting a newer switch in the future just to add the ground, but there are many situations where this arises and grounds not used.
Some switches today are designed so they are insulated and do not require grounding, since they cannot produce any possible danger of electric shocks.
Let me know of anything further needed,