What GOG games can be played windowed with mouse only?
And that without using any kind of hack or mod. No Dosbox games please.

Open Transport Tycoon Deluxe! You can even dynamically resize the window!
...
Oh, right, that's not on GOG.
Why is it not on GOG?

I can't guarantee thay these are strictly mouse only (that is, no keyboard input required ever... i'm thinking when saving, for example) but they come very close... off the top of my head I may say:

Age of Wonder series
Baldur's gate and Icewind dale series
Defcon
Disciples series
Eschalon series
FTL
Heroes of M&M series (from 3 onward they are native Win32)
Legend of Grimrock
Papers, Please
Sacred gold
Shadowrun series
Simcity series
Sword of the stars: the PIt
Tropico series

... a TON of those in the point-and-click category

... and a TON i'm forgetting; no, really, there are many but it's a bit hard to do a comprehensive list

blazblue calamity trigger

I'll mention Bejeweled 3 because, while not on GOG, it's free right now on Origin.
Well, off the top of my head, I think maybe Banished, and the Roller Coaster Tycoon series (that's not DOSBox, right?)