Can I connect an Apple Watch to my iPhone without syncing activity data? Or is there another way to roll back Activity data?

So - as a direct answer to your question - no, unfortunately it doesn't appear possible to do what you're asking.

Now for a longer, more descriptive answer. After carrying out some research and performing some of my own tests, it unfortunatley doesn't appear that it's possible to simply remove a single exercise whilst also deleting the corresponding award earned from it; removing the exercise from within the Health app leaves the award which can, as you mentioned, still be found within the Activity app. The following threads posted to the Apple Discussions forum were posted by users who also had a similar problem - confirming the above:

https://discussions.apple.com/thread/8257414

https://discussions.apple.com/thread/250261634

https://discussions.apple.com/thread/250009083

In addition to this, it also doesn't appear possible to use the backup of an Apple Watch to simply replace the Activity data/rewards on the Watch's paired iPhone; that said, I'm not 100% sure whether the Watch backup itself actually includes any Activity data itself, or whether this is only retained on your iPhone. It appears that the only way to resolve this is to reset your Health data - which is far from ideal, but appears to be the only resolution at this time.