You could just disconnect the tone pot, as suggested., since it loads the pickups too, but you could use a so-called "no load" pot which is switched off in the 10 position.
How is changing the tone cpacitor going to do anything? When you want a bright sound the tone knob is on 10, and so the tone pot is in series with the tone cap blocking its effect. So changing it will not make much difference.
Either way, a pedal may be your only choice other than replacing the pickups. If the stock electronics make the guitar sound too bassy, then there's not much you can do. Replacing the pots for higher values or changing the tone capacitor may help (I'd remove the tone pot entirely from the circuit, but that's me), but if it doesn't then you're stuck with the pedal or replacing the electronics. Or dumping the guitar.
GBT