Do it later, after they've turned brown. You should do it every year.

Let them keep growing. Mine are still sending out new fronds. You will have plenty of time to clean out weeds later in the fall.

They grow wild along side the road and do fine. That was where we got most of our asparagus when I lived on a farm in Michigan and the same is true in Colorado. But I do know they still do better without the weeds. We knew where to find them by the stalks that were left over the winter months.

You might try mulching heavily on top of the weeds. Shouldn't hurt the asparagus and should slow the weeds down. It shouldn't be too hard to move the ferns aside temporarily.

Mine is actually sending up a few new spears!