Can I travel abroad in Shanghai with my Hong Kong ID card?

Of course. But it depends on whether you are a permanent ID card or a temporary residence permit in Hong Kong.

If you are a permanent resident and hold a Hong Kong passport, you basically don't need to apply for a visa. You can go to the sea cucumber group. Regular price travel agencies will not make any difference.

If it is a "Hong Kong temporary residence permit", that is, a non-permanent identity card, it is still a mainland passport, or a visa is required.