So, I ended up buying an S10 Al Jet Black 46mm. I went through all the settings and there is no way to stop the speaker from playing music. So, if you accidentally hit play in a music app, music will play on your watch. On the S9, the behavior is different, it will ask you to connect to a device and if it can't find your headphones, it will not play, keeping you from potentially embarrassing yourself. Just an FYI for anyone else that listens to music on their AW while exercising, commuting, etc.
Edit:
Here are the S9 45mm (left) and S10 46mm (right), both cellular. The cellular model on the S10 now has a silver circle instead of red circle on the S9.
I have the Modular Compact watch face. I find this to be the best for all-around use (for me). I can easily access music via the Suggested (formerly Now Playing) complication and the seconds are really helpful at the gym so I can see my rest time easily.
When you click on Suggested/Now Playing, the S10 automatically begins playing music (even if Silent Mode is on). On the S9, it asks to connect to a device and I much prefer this behavior as you can very easily accidentally press the Suggest/Now Playing complication. Similarly, if you turn the volume all the way down, then you can't hear any notifications. I find it amazing that no Apple engineer or PM thought it wasn't necessary to have a way to turn the speaker off.