I have both a 610 and a 310NG. I have never tried to fire either without moon clips.
Being rimless they will not eject without the moon clips.
I have fired way more 40 S&W through both, than I have 10mm. You can count on 40 S&W not head spacing on the front of the case.
My advice. Leave the Half moon clips in the bag in the S&W box. Make an order with TK and get several Full Moon clips, and enjoy your 610 using moon clips as it was meant to be used.
http://www.moonclips.com/
NOTE: The 610 moon clips come in 2 versions, the Round Hole Center, and the Hex Center. No big deal unless you are using a Moon Clip Tool to load the clips. They use different Arbors. The Deluxe Moon Clip Tool extra Arbors are $5 each.
http://www.mooncliptool.com/
I have had my 610 for 20 years. They are a great revolver.
I have shot lots of 40 S&W through mine over the years.
For carry ammo you will need to do some research. Most 10mm factory loads have really been watered down over the years. The 175 Winchester Silver Tips are probably the easiest to get pretty much full power ammunition for carry. After that you will need to go to a specialty ammunition company for Full Power ammunition, like Buffalo Bore.
Bob