What I have done (on many an older rig I have brought home from time to time) is remove the window, replace the putty tape under the window flange, and reinstall the window.
to remove the window, there is a rubber insert that snaps into a channel around the window frame. Remove it, under it is many screws with 1/4" heads, remove all them, then remove the window. You may have to pry it out a little, be sure you don't pull the siding away with the window.
when the windows is out, use a ballpen hammer to "adjust" the screw holes so they are flat again. when installing the window back in, don't torque down the screws so bad it distorts the window frame.
Once I replace the putty, I use sealant in a caulk gun, made for gutters across the top, and down the 2 sides. I don't put it on the bottom, so the window seal can drain if water does get behind the flange.