Wearing your Apple Watch while exercising or working out without your iPhone nearby is fine…but battery drain will depend on a number of factors.
If you have a straightforward non-cellular Apple Watch, it will have very little impact on battery life. If you want the watch to stop Bluetooth and Wi-Fi looking for a signal connection, you could put the watch in Airplane Mode where the GPS will still track but again the impact will be negligible. This would obviously stop you from listening to music stored on your Apple Watch as you wouldn’t be able to connect AirPods (with Bluetooth turned off).
If you have a cellular Apple Watch, it will switch to your cellular connection as soon as you are away from your phone, as long as the watch cannot detect a Wi-Fi signal (if there is a signal).
I work out with my watch in this way every day for a 5K run. It’s great that I don’t have to carry my iPhone with me while running, but I can still be reached in an emergency. I then listen to music in two ways…either listening to music stored on my watch (played over AirPods) or listening to music streamed from the podcasts app or Spotify. Streaming over cellular has the greatest impact on battery drain…understandable given that you are using pretty much every single feature of the watch at once (cellular, tracking, streaming/audio playback).
That being said, I did a 45-minute 10K run on Monday, without my phone, on cellular, and streaming a podcast. I left the house with about 85 percent battery, and after the run, I still had 54 percent, which was about the most I could do to drain the battery.
If you are just doing a workout and the watch is non-cellular and not listening to the music, the battery drain will be negligible over standard use