As far as I understand from your explanation, the problem in your case comes from the fact that you do not know how to reference the particular tooltip in order to change its size.
If so, I suggest to do the following:
1) Hook up the OnClientShow or OnClientBeforeShow event.
2) Find the best way to detect the tooltip in your case, e.g check its text (get it through the get_text() method) and compare it to the text of the partcicular tooltip. If the text is the same, this is the tooltip you need and you can change its size through the client-side API mnethods. If it is not, do nothing.
I hope that my suggestion is helpful, let us know in case you need further assistance.
the Telerik team