Are there any third-party bands for the Apple Watch that don't require any adapter. I have a 42 mm SS AW 2.
You sound like a new Apple Watch owner. Hope you like it. I have a 42mm SS AW1 and still love it.
If I understand your question, any 3rd party silicone sport band for example won't require an adapter since the locking tabs are built into the strap. Now a days there are third party bands sold with classic style adapters included with the strap so no need to buy them separately. This wasn't true when the watch first came out. I think you'll find the majority of third party bands sold in the various styles are now supplying the lugs (adapters/connectors).
As of a number of months ago Apple through another party sells OEM classic adapters/lugs to authorized band developers. These will probably be those that offer more expensive quality bands. Other less expensive alternative bands probably have their own adapter manufactures. Apple has specific requirements for its authorized band developers such as meeting strap tolerances (width, thickness, strength, etc) and meeting screw tolerances for mounting the straps onto the lugs. Most importantly I think is the loctite adhesive to be used. Those little screws used in the classic style adapters will come out from daily vibrations if not properly set with adhesive.
From posts on the forum you will see that some people who have bought 3rd party bands have reported problems with straps separating, lug screws coming out and watch cases falling off as a result. Even people buying the 3rd party link and milanese style bands have reported various issues. If you're considering buying a third party band, do research on the brand and company selling it. You will sometimes get what you pay for in materials, workmanship, and/or warranty. Things have gotten better with 3rd party bands but still do some research.