Yes, wash gently, lubricate and push back in. Do you have any sheep neighbours that might have a 'spoon' that helps hold a prolapse in while they settle.
The other way, with sheep, one of my goat's hair would be long enough, the other not, is to tie pieces of yarn, to her hair, across her tush, so you make a series of bars to try to hold it in place.
The vet might put a purse string stitch in - you hear people recommending doing this with baler twine and no anaesthetic - all I can say is that those people are always male and have insufficient empathy