I go for walks and sometimes I have random thoughts I want to capture but I don’t want to have to fiddle with my phone which is usually in my pocket.
Is there a way to start and stop a recording using Siri?
I just tried using Siri to capture a Voice Memo but it only opens up the app - it doesn’t start recording.
Short answer: no.
Longer answer: you can keep your phone in your pocket and use Voice Memos (or a 3rd-party app like Just Press Record) with an Apple Watch. But you’ll still need to physically tap a button.
I presume that at least partly for reasons of privacy to others Apple doesn’t want there to be an easy way to surreptitiously record audio, and on the iPhone there’s a VM overlay displayed when in use, the Watch shows the glowing red Record button, and Siri cannot invoke recording.
Is the format important? Did you particularly want to record as audio or would capture into text be ok?
If you ask Siri to create a note then you can dictate some text without having to unlock your phone.
Thanks to @bowline and @stu_w. I hadn’t thought about capturing as text.
I tried both ways. On one hand, I could use my watch to start and stop. Didn’t think about that. But creating a text note is so simple. Don’t have to touch anything which is really nice.
Glad that helped 
Not sure how much text you can capture with the notes dictation, I’m suspecting not much before it times out. Also, if you leave anything of a pause it stops. Not sure if there’s options to “Hey Siri, append to my last note…” .
For capturing a quick thought about something while I’m out I generally use reminders so I can get it to nudge me some time later. By the time I’m in a position to do anything about it, the fact that I’ve had the thought & made a note about it has probably been long forgotten. That might be just me though. 
I use Drafts via my watch for this. You can set it to auto dictate when you open the watch app. Drafts manages to avoid the dictation timeout that normal Siri dictation suffers from
Except the OP wants to take notes without opening a phone. Can you invoke endless notes in Drafts from a locked, pocketed iPhone just by invoking Siri?
Short answer no.
Longer answer- phone only almost. You can hail Siri to run a Shortcut- which opens a new dictation Draft. You can then dictate your note… but you need to click ‘create’ on your phone.
Same with the watch you can do it all via Siri right up until you need to create the note and end the dictation.
Tbh I use a one tap Drafts complication on the watch and save with one tap. Close enough to magic for me and I can do it whilst running so it’s pretty user friendly
So pretty much what you said Bowline lol