This solution occurred to me:
For Each cell In Selection 'Determine current reference type
Select Case cell.Formula
'xlAbsolute
Case Application.ConvertFormula(cell.Formula, xlA1, xlA1, 1): ref = 2
'xlAbsRowRelColumn
Case Application.ConvertFormula(cell.Formula, xlA1, xlA1, 2): ref = 3
'xlRelRowAbsColumn
Case Application.ConvertFormula(cell.Formula, xlA1, xlA1, 3): ref = 4
'xlRelative
Case Application.ConvertFormula(cell.Formula, xlA1, xlA1, 4): ref = 1
End Select
'Cycle reference type
cell.Formula = Application.ConvertFormula(cell.Formula, xlA1, xlA1, ref)
Next