Radish pods ripen over time, starting from the bottom. Given the number of seed produced by each plant, you don't need to wait until all pods ripen on the stalk. I assume that you rouged out off types, leaving the most vigorous and healthy radishes. You can pull the whole plant with some soil and heal in elsewhere or bareroot and hang in a cool shady site to finish seed maturation. I usually clip off the upper section which will never fully ripen anyway. Watch for pod shattering -- bagging will minimize seed loss at later stages.
The bed I planted with the black spanish radish will be used for squash next month so I had plenty of time to let them ripen in the bed. The radish were planted in fall and were pulled at the end of May when all the seed pods were brown.
As Marsh said, they do ripen gradually.
Put the seed heads (and parts of the stem too)in a big bag. Black trash bags work fine. Walk on the bag to crush the seeds out. You will punch some holes in the bag from the tough stalks and pods but it doesn't matter. The seeds won't be damaged (mostly) and you'll get most of the seeds released from the tough pods without sore fingers. Pour the resulting seeds etc into a bowl or bin and toss to release the chaff.