Disclaimer: though I'm anonymous here, I'm the author of both Astro::Coord::ECI and Astro::SIMBAD::Client.

Astro::Coord::ECI and friends are a bit heavyweight if all you want to do is convert degrees to radians. The actual code to do this is two lines:

use constant PI => atan2 (0, -1);
sub deg2rad { return defined $_[0] ? $_[0] * PI / 180 : undef }

As for computing angles, I will not recommend a specific module. I will say the initial implementation of Astro::Coord::ECI->angle() naively used the law of cosines, but I had to switch to the law of haversines after trying to compute the closest passage of a satellite to a star and having the law of cosines blow up.

All I can say about Astro::SIMBAD::Client is that it is a mess. Sorry. There are a number of ways to get the data, the SIMBAD API changed over time, and, well, what can I say? It badly needs a simpler interface. It takes me 30-some lines of code just to get the position and proper motion of a star. If you decide you want to wrestle with it, you can contact me at wyant at cpan dot org.