Hi,
First, could you post some pics of the scooter? It will help a lot giving more accurate answers.
From the data you gave us, I'd say you'll be just fine using this 37A controller, given the fact that your battery is a 37Ah one, that gives a C rating of around 1C which is really not much even if you have really bad quality battery cells.
So, electrically speaking, this should work, no problem.
As Balmorhea said, one issue might be the battery monitoring system if this thing is using a lithium battery (and it's likely to be lithium given the fact that 37Ah is a lot of capacity, so that'd be huge and heavy with lead acid), in which case it might cut the power when you'll try to accelerate. Or not, depending how the people who installed the monitoring system programmed it. My guess would be that it will work, the power difference is not that crazy.
So anyway, you can try, it there's no major red sign here. :wink: