Hannah, the new Northern Counties champion, has scores of 79-84 for 163, which left her in joint eighth place the Irish leader, Gillian O'Leary (Cork).
Teenager McCook is two shots ahead of Leona Maguire (Slieve Russell), the defending champion and a member of the GB and I team for next month's Curtis Cup match at Nairn GC.
On a very windy day, particularly for the first round, all the Scots in the field made the cut.
LEADING SECOND-ROUND TOTALS
Par 148 (2x74) CSS 80 79
156 Gillian O'Leary (Cork) 79 77
157 Emily Taylor (Eng) 85 72
158 Deirdre Smith (Co. Louth) 83 75
160 Mary Dowling (New Ross) 81 79, Lisa Maguire (Slieve Russell) 81 79
162 Maria Dunne (Skerries) 80 82, Charlene Reid (Royal Portrush) 79 83
163 Joelle van Baarle (Bel) 84 79, Hannah McCook (Grantown on Spey) 79 84
SELECTED SCORES
165 Leona Maguire (Slieve Russell) 82 83.
166 Eilidh Briggs (Kilmacolm) 82 84.
169 Megan Briggs (Kilmacolm) 87 82, Alyson McKechin (Elderslie) 83 86.
171 Jessica Meek (Carnoustie), Gabrielle Macdonald (Craigielaw) 86 85.
176 Sammy Vass (Tain) 83 93
Players with aggregates of 176 or better qualified for Sunday's play.
Thanks go to Colin Farquharson for the report.