Ugh, honestly I feel your pain. I spent way too much money trying to find a flash that didnt make my a7C II feel like it was gonna tip over. Most compact options still feel like bricks once you actually start shooting. I tried the Sony HVL-F28RM External Flash and while it looks sleek, the recycle time really frustrated me during fast street shoots. You miss shots waiting for the damn beep. If you want something genuinely small tho, check these out:

• Sony HVL-F20M External Flash
• Its super thin. Like, actually pocketable. But ngl the power is pretty weak and you cant rotate the head, only tilt it up.
• LightPix Labs FlashQ Q20II Manual Flash
• This one is cool because the flash head pops off for off-camera stuff. Unfortunately the build quality is kinda plastic-y and I had issues with the battery door staying shut after a few months. Since youre heading to Tokyo in five days, you probably want something reliable. Tbh Im still searching for the one but the F20M is probably your best bet for size alone. Just dont expect it to light up a whole room... its more for a little fill light in the alleys of Shinjuku. Have a blast in Japan tho, super jealous!

Regarding what #2 said about "Ugh, honestly I feel your pain. I spent..." - yeah I totally get that. I am always so worried about snapping the hot shoe off if the flash is too big or top-heavy. Since you are on a budget, you might want to consider the LightPix Labs FlashQ X20 for Sony TTL. It is super tiny and way cheaper than the Sony brand stuff, which is nice if you are trying to save cash for the actual trip. Just be careful though, because it uses AA batteries and they can die pretty fast if you are shooting all night. Before I say go for it... what are you actually planning to shoot in Tokyo? Like, is it mostly indoor cafes or people on the street? You really gotta make sure to check the recycle times because small flashes can be slow. I would suggest bringing extra batteries just in case. Better safe than sorry, especially on a big trip!

I had the exact same issue when I first started travel photography. Carrying a massive speedlight on a small body like that feels like putting a truck engine on a bicycle... it just doesnt balance right. For my last trip, I picked up the Godox TT350S Mini Thinklite Flash and it was a decent middle ground for the price. Heres my experience with it:

• It is incredibly light and wont make your wrist tired after a day of walking around.
• Uses two AA batteries which is handy because you can find those anywhere in Tokyo if you forget your charger.
• The TTL works fine with Sony bodies so you dont have to overthink settings. It lacks the power of the bigger models and the recycle time is definitely slower, but for street shots or filling in shadows, it gets the job done. Honestly, i usually just keep it in my bag tho because it takes up almost no room and costs way under your 200 budget.