Assistance with hardware selection

I'm afraid your options are very limited in terms of low-profile operator handles. Your best option is probably going to be the 39-205, which folds down. We also have the 39-102, which is a short-profile T handle.

That's about it, unfortunately. Your operator can't take a new cover, so you won't be able to get a handle that nests in the base. It's also important to note that no matter how low-profile the handle is, it can never go lower than the spline of the operator itself, which sticks out quite a bit. There's not really anything you can do about that.

If you're trying to install new blinds for this window then that spline is always going to get in the way. You would have to install the blinds in such a way to make way for the operator, not the other way around.

There is no operator with that kind of low profile that I know of, unfortunately. All modern operators are designed to have that spline stick out a couple inches from the base. There was a time when manufacturers made operators that had a hole instead of a spline, to accommodate a "male" handle, but that design has fallen out of favor and is very, very uncommon now.

I am very sorry for the inconvenience. This is just the way operators are made these days.