You can customize the initial shortcut (maybe use Alt+S).
If your style names are short (i.e., h1, h2), Alt+S, type h1, Enter.
Or if they start with different letters (i.e., abc, def), you can do Alt+S, <type first letter of desired style name>, Down Arrow, Enter.
That doesn't seem too much worse than remembering a different shortcut for each style.
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