Saying "Modeh ani" with dirty hands

Hi,

We are supposed to wash our hands ritually, with a cup, each morning, as we have discussed elsewhere. Even prayer is prohibited before this washing. However, one may recite the opening sentence of "Modeh ani", because it does not include the Name of Gd.

(Mishneh Berurah 1:8)

Have a great day,
Mordechai