Yes this is fine. No need to make another wudu and use Miswak again right before going to bed, unless you broke your wudu after your Isha’ prayer. As for using the miswak, I don’t remember any authentic hadeeth stating that it should be used as a sunnah.

If I sleep soon after praying isha (used miswak and with wudhu), will it satisfy the sunnah of using miswak before sleeping and sleeping with wudhu or do I need to make a separate wudhu nd miswak once more prior to gng to bed?