Gearing should be the same as tyres get thinner.
You say you are changing because bottom gear seems too high, then you later say gearing should remain the same as tyres get thinner. I have just taken 16" wheels off my wife's si because of harsh ride and fitted 15" and guess what, the gearing is the same and speedo is reading exactly same as with 16" on. Ride is much better and tyres are a very reasonable price now with loads of choice.
17" wheels are not homologated size for the mk2, the sizes that are legal on your jazz are on the sticker on drivers B pillar.