Even if they are out of options you may still designate without waivers. However, you can not assign them back to the minors if a trade doesn't materialize.
If you designate them without waivers and do not assign or waive them afterwards, the AI will automatically RELEASE them after 10 real life days.
If you wait until the DAY AFTER the transaction deadline (EXAMPLE: deadline is at 3AM on the 23rd, you wait until sometime AFTER the AM cycle on the 24th) to make the "designate without waivers" move and end up not being able to trade the guy, you can just add them to the BL Roster on day 9, which will be the "roster expansion" day (provided you have the cap space, of course).