I probably now have to implement all other arithmetic operators used in that JS code as above.

I can't come up with a better solution ... but if you were to use a perl whose ivsize was 4, then I think (not rigorously tested) you could take care of it with a simple use integer; at the top of the script.
On perl-5.38.0, built with just that configuration:

D:\>perl -V:ivsize
ivsize='4';

D:\>perl -le "print 1169367104<<5;"
3060008960

D:\>perl -Minteger -le "print 1169367104<<5;"
-1234958336
[download]

Cheers,
Rob