OK, I think you might have taken yourself down a slight side-track.
Presumably, you are only running Puppeteer queries when you really have to?
But in any case, you can certainly continue to run those on a server. Personally, by the way, I'd choose to run Node-RED and any web-scraping scripts on a Linux server as you will certainly get more bang for your buck than using a Windows Server as you appear to be doing (though obviously, that somewhat depends on what support skills your organisation has).
We also don't know how time-critical the running of these queries are. If they aren't time critical, you could consider spinning up a Node-RED instance when needed and then shutting down again. This is likely to keep your AWS costs lower.
I'd still opt to run the queries in a separate microservice myself though - that would be really easy then to manage including faster startup times if you decided to only fire them up when needed.