It's probably worth mentioning since you "dont like the sounds of the reeds" of an accordion that high quality reeds are a pulse noise source (similar to reed and brass instruments and the human voice box) that can be shaped in a number of ways in a "vocal tract" in order to get different characteristics. The Russian "Timbre" group uses instruments (bar one, often playing lead because its sound is a lot more cutting) where this kind of resonance carving has been put to an extreme.
But a similar flute-like quality in differing degrees is achieved by "cassotto", a resonance chamber or canal coming in a large variety of executions and sounds that contribute a lot to the different characteristics of high-end instruments.
The usual sound quality associated with accordions is that of a 2- or 3-reed "tremolo" achieved by a sort of chorus effect between several reed sets tuned slightly to awfully different. Accordions built to accommodate classical music usually don't use tremolo at all, cf this rendition of the Goldbach variations by Lena Rist-Larsen. Most high quality accordions featuring a "converter" on the left hand (rather than just the default bass+chord layout called "Stradella bass" and suitable for accompanying music with reasonably simple harmonic framework) do have cassotto and little to no tremolo.
If you want to play keyboard music, somewhat counterintuitively it makes sense to use a "chromatic button accordion" rather than one with a piano keyboard on the right side. The left hand has to use a CBA-like layout in free bass mode (one note per button) anyway and the larger hand range and overall range of a CBA is rather useful for keyboard music since passing voices between hands is not feasible in a manner similarly innocuous as on the single manual of a piano.
The downside, of course, is that this is a full polyphonic instrument in its own right, and the playing technique, articulation and sound production is significantly different from a piano and more similar to that of a reed organ. And the good instruments don't come cheap either.
But, well, if you cannot find anything better, there are a few interesting variants not really fitting the standard clichés.