As a rule there will be a large electrolytic cap alongside the keying transistor. Might be 220uf, maybe larger.
Maybe. Keying circuits are not all created equal. But if you can identify a cap over 220uf that is wired to the "cold" side of the relay coil, unhooking it should do the trick.
Just one problem. You may still need a small cap, 4.7 or 10uf wired where the larger one had been to prevent the relay from chattering with modulation. An amplifier with a SSB switch will generally have a diode in parallel with the relay's coil. This is to catch the reverse-polarity "spike" of voltage coming out of the coil when you unkey. A keying circuit built with that big capacitor in the circuit all the time doesn't need it. Remove the cap, and now you need one of two things. A smaller capacitor to reduce chatter, or a diode.
And if there is no large cap like that connected to one side of the relay coil this means the keying circuit is different from the one expected.
73