What would you recommend to take as a secondary skill for a battlemage/conjurer type? Primary skills are one-handed and summoning. Magicka pool is about 200, so he will require lots of enchanted items to cast destruction spells, so maybe archery is more convenient, but then, a battlemage with a bow... I don't know.

Conjure Bow

The question was perk-wise. Archery, then?

It would fit with your current conjurer type, surely he would get to learn that which he summons?

I agree with conjure bow but also consider conjure sword for your one handed use. Also consult the sneak perk tree for the 3x bow damage sneak. I'm a higher level archer with this perk. The bow is darned effective.

Conjure sword and bow are clear, but sneaking may be a problem as battlemages use heavy armor. I am not sure it can be muffled. I was thinking more in terms of taking out opponents at range while being in open, when need arrives, and what would a battlemage use in that case. The Conjure Bow spell is a good reason to take archery.

There is a muffle perk to reduce your noise up the sneak tree. The sneak perk may be useful to you just for the 3x bow aspect & not for the sneak itself. I find the 3x while sneaking to be very useful. If you are in sneak, you can snipe from quite a distance. Unlike OB, the bows in SK shoot like rifles so are effective and easy to hit with from amazing distances where your heavy armor won't give you away.