I think a lot depends on the oil. You might try using grapeseed oil for less flavour. Or mix it
with Extra Virgin Olive Oil. Perhaps the best start would be to determine how tart you like it based on proportions of oil to acid and depending on the acid you use. Try somewhere between 2 and 3 oil to one part acid. Just whisk the oils slowly into the acid.
Acid could also be a white wine vinegar. But it you add some good quality Dijon mustard (like Maille), it is a good emulsifier and tends to balance the flavours a bit.
Mine almost always starts with finely diced shallots. I use lemon juice or various vinegars. You may find rice wine vinegar much milder in flavour. I also use a variety of oils in combination with grape or olive...my favourite is hazelnut, but also pistachio, avocado, ,,,, Then some herbs...basil, tarragon, etc. Plus lots of sea salt and fresh ground pepper.
Try some rice wine vinegar. Unseasoned so you can add your own flavours. I'll bet you'll like its mildness.
And you don't want to overwhem the greens with the vinaigrette. Just a light tickle so that each leaf has a drop.