Although there is a module called SVG to generate SVG files, I'd probably just use XML::LibXML. The SVG module doesn't seem to gain you much.

Rather than directly trying to generate Adobe Illustrator files, I'd look at converting the SVG file you already created. If you have Adobe Illustrator on the same computer you'll be generating these files, it's capable of importing SVG files and saving them in its native format. If there are a lot, then it can apparently be automated.

An alternative way to do the conversion would be to look at using convertio.co. I haven't tried it myself but it claims to be able to convert between these formats, and it offers an API. Shouldn't be a lot of work using JSON::MaybeXS and HTTP::Tiny to submit your SVG files to their API and receive Adobe Illustrator files.