There are two types of starter: the new electronic ones and the older gas discharge ones. The electronic ones generally cover a wide power range so yours is probably a discharge type. These consist of a small gas discharge lamp with a bimetal switch inside and they work like this:
1) You switch on; the tube is cold. Current flows through the ballast inductor, one tube filament, the starter lamp and the other filament.
2) The tube filaments heat up but this in itself is not enough to get the thing going. The bimetal switch in the starter is also heating up.
3) The bimetal switch opens, breaking the circuit. The ballast, being inductive, responds by generating a high voltage spike. It's this which causes the tube to strike. Meanwhile, the lamp in the starter has gone out.
4) The bimetal switch in the starter cools down and closes but, with the main tube conducting, there isn't enough voltage across the starter to re-ignite it.
From this, you can see what can happen if you put an UNDERSIZED starter in. If the running voltage of the tube is high enough to re-ignite the starter, the thing will try to restart the tube over and over again. This also happens as tubes age because their running voltage goes up.
It is less obvious what might happen with your oversized starter. If it's significantly oversized it might overload the tube filaments.
Since yours is a borderline case it will probably work but why risk it. Starters are cheap.
