It would be helpful if you could tell us what kind of grasses you have.
To start ~ I would not cut them down at this time of the year. In your zone they have probably made much of their growth already. Please, someone chime in from a more appropriate zone on this part of the question.

You could do a few things this year without harming the grasses.
1. Try to trim out some of the older dead stems to tidy up the clumps.

2. you can 'prune' off the new shoots that are crowding your walk. A bit like pruning a tree, taking off a few stems here and there won't hurt the grass at all.

How about a picture of the problem area?

Take a look at your grasses. You will probably notice that the middle of the clump looks the 'rattiest'. Then When you divide them, only use the outermost sections. I would take some small divisions now, and test your surgery techniques. Just pot some up and keep them in a shady spot until established. If they survive, you might just want to get rid of the large clumps, and start over with your smaller divisions.