To work the spawn, most of the regulars I've seen tend to para tame and then set the tamed cu on wild ones: I use a char with GM mage/eval to ensure the pup is fixed firmly and then invis once I start a tame. You need to get into the rhythm of it and anticipate when the para will drop so you can stop holding down the tame key and re-para.
You can also lead tame normally but it can be boring walking around the same circle for weeks
You do lose an extra 4% from skills after para taming, so I'd use a normal lead tame for anything I wanted to keep or sell.
I also have a method that involves quickly killing the pups and taming anything useful. But it's only useful if you can kill the pups much faster than through taming. I run a disco/voke tamer there. You do need to watch your karma though, especially as paragons always seem to be the first critters to notice! I've seen a few folks think "I'm ok, the pixies didn't hit me" then walk smack into a para cu sidhe.... Not pretty... Just watch other tamers don't gather and wait to take advantage if you go on a pup killing spree.
Wenchy