Do the non-weapon weapon skills count toward circling weapon skill requirements?

Specifically, if melee mastery, missile mastery or offhand weapon are 1st, 2nd, or 3rd highest weapon skills will they be the skills used to determine eligibility to increase in circle or will they be skipped over in favor of weapon weapon skills?

Offhand also does not count.

>I was afraid that may be the case. Thank you for the replies

Why afraid? Target magic will always be your best friend, but weapons are cool. Some invasion critters are heavily resistant to elemental damage. Sometimes you wanna kill a Moon Mage without having to worry about Shear.

Embrace the warrior side as well as the mage side. Honestly I'd recommend you train 4+ weapons anyways: a thrown weapon, crossbows, a huge two-handed melee weapon, and a light/quick melee weapon.