Actually I now noticed that it actually says so on the Trafi web page:
Autojen, joiden ainoa käyttövoima on sähkö, perusvero määräytyy päästötiedon 0 g/km mukaan.
I hadn't noticed that before and obviously the person I asked this about earlier hadn't either.
The downside is that electric-only vehicles are blessed with a separate tax to counter the fact that they don't use any heavily taxed gasoline. That amounts to 0,255 cents per day for this vehicle, while the base tax is 0,118 per day. 136,14 € total per year.
In any case, at least I'm not getting any extra punishment for converting such an old vehicle. As a bonus I'll save some money in the yearly inspection, since the vehicle needs no emissions tests.