Not sure I have a Handwash cycle, unless it is buried in the Special Cycles and I haven't scrolled through all of them. I have used Delicate cycle for Delicates and nothing was ruined nor inadequately cleaned. Note you can lower the spin spin and agitation time if you are concerned that the default setting is too rough.
In the photos I posted, you access the Specialty cycles by pushing the silver button under the LED display, then you rotate the big silver selector knob to scroll through them. The 70 series has even more cycles, like Stuffed Animals. The 60 has Jeans, Pet Beds, and a few others. Hopefully the PDF user manuals on Elux website will guide you, as long as they didn't produce one manual to cover 60 and 70. If you like I can scroll through the Special cycles and make sure I listed them all. The "clean washer" cycle is also found in the Specialty cycles. The machine reminds you after every 50 washes to clean the machine. Can be done with bleach or the Tide washer cleaner product; I use the latter.
The machine lets you customize a Favorite cycle, but I don't bother. If you change the defaults (temp, wash time, spin speed) from factory settings, it remembers your choices and uses them the next time you select that cycle (so you have to pay attention if you want to use different settings within the same named cycle).
When I bought in Nov 2014, there were a lot of rebates. $275 from Elux, $40 from the gas utility, $60 from the water district. The federal guidelines for water use changed in the interim and my 60 would no longer qualify for a rebate (nor would any Elux) in California now. The Elux rebates did not apply to the 50 or 55, so that that higher price of the 60 set was almost negated by the rebates. I bought from a local appliance store that sells nearly every major brand, SQ included, and ALL of the employees---who are allowed to buy at dealer cost---have Elux at home.