This entry from the
Dictionary of the Scots Language might help. It has references to period documents! *is all excited*
S(c)hire, n. Also: s(c)hyr(e, s(c)hir, scire, schyir, schier, s(c)hyer(e, schyier; scheir(e, sheir, scheyr, scheyir; s(c)hair, shayr; (scyre, skir-, sire, seihire). [ME and e.m.E. schire (Ancr. R.), sher (c1450), shiere (1549), sheere (1615), OE scìr str. fem., = OHG scìra care, official charge, of the same ulterior origin as Cure n.1]
1. a. In earliest use: A subdivision of the royal demesne, in which the services and duties owed by the tenants were overseen by a royal grieve, lord, thane or prelate.
For full discussion, see G. W. S. Barrow The Kingdom of the Scots (1973), Chapter 1.
Also attrib. with stane. [Et schiram de Kirkaladunt et Inneresc minorem, cum tota schira de Fotriffe et Muselburge;
1070–93 Early Chart. 9.
In Coldingamscire;
c1100 Ib. 17.
Scyram de Kircalethin; … Scyram de Gelland … scyram de Gatemilc;
1154–9 Regesta I 182, 183.
Preterea do eis communem pasturam in sire de Erdos sicut habent in sire de Callin;
1153–62 Ib. 215.
Kinninmoneth cum tota schira;
1160–1 Ib. 218.
In tota skira de Kilrimund;
1163–4 Ib. 260.
Carelsira;
1153–78 Laing Chart. 1.
Vicecomitis et prepositis Strivelinis scyra; 11..
Reg. Dunferm. 10.
Hadigtunes scyra;
Ib. 88.
Kylrimonthschyr; 11..
Reg. St. A. 132.
Foregrund seihire;
c1163–4 Ib. 187.
Ad sectam et multuram tanguam ad molendinum scyre de Lundors;
1261 Lindores Chart. 142.
I cut the entry there as the rest is after your time.
Perhaps calling Aberdeenshire 'The Scyre of Aberdeyne' or 'The Schyr of Aberdeyne' would take away the modern flavour of the word? Again, just a thought. The spelling of 'shire' shown for the period might be to difficult to understand for modern readers, though. Maybe the 'Schyre of Aberdeyne'?