The service manual shows a washer on the drain plug - none on the fill plug.
I have been using copper washers from my VW days on both.
It is very hard to find a genuine "crush washer" these days (I've seen them listed for Subarus) ...."Crush Washer"= a washer that required only moderate tightening because it 'crushed' to form a nice seal. VW beetles used these on the oil drain plugs - a copper skin wrapped a fibre center that crushed when gently tightened.
The deal is - they seal perfectly without needing to risk overtightening a drain plug into a soft alloy case! And, no they could not really be used a second time.
No longer able to find these so,- softer metals, like brass or copper can work - or the washers with a rubber backing that are compatable with heat and petroleum products. (Good luck finding these!) Or a rubber washer that's up to the heat and oil.
181 ml is the amount of 80W90 gear oil to put in, once you drain.
This is just a hair more than 6oz....... which is 3/4 of a cup (buy your wife a new one after you put gear oil in her measuring cup)
Put 3/4 cup of new gear oil in a squirt bottle, or pick it up with a syringe - squirt it in the fill hole. Screw in the fill plug, snug gently....with or without a washer, and Bob's Your Uncle~! you just completed an important service on your scoot!
I'd do this ASAP - before going any place on your scoot. Now that you're changing your own gear oil - that quart bottle will last you quite awhile.....3/4 cup at a time!
If you see the oil again, or smell that hot smell - stop - trailer it to the dealer!
Stig