I've developed software (some of which use SysTray icons w/tooltips). The
application may be looking to see what the current text is displaying...and,
the code may be set up to update it as needed (again, depending on the app).

Using any low-level tools (to modify the app) could cause serious problems.
For example, if the pop-up text contains a status message (like "Currently
Connected" or something like that), the app may be looking to see if the
status is currently in the tooltip... if it's not, it may execute additional
code to update it. If it can't update it, it may perpetually keep trying,
wasting CPU time, etc.

Or...it may be a simple tweak that doesn't cause a problem.

Regardless... even knowing how to manipulate the systray with the Windows
API, I personally would never try modifying the app itself.

HOWEVER:

It may be simpler than that: In the folder where the app is located, check
for an INI file (or a config file, etc.). This info MIGHT be in here
(doubtful, but you never know). Another place to check is the registry (a
bit more dangerous).

The two typical places where apps store their registry software settings
are:

HKEY_CURRENT_USER\Software\<Company Name>\<Product Name>

and/or

HKEY_LOCAL_MACHINE\Software\<Company Name>\<Product Name>

You may see an entry in the INI/config file or the Registry that has this
information, or, some sort of toggle for the tooltip.