You don't have to worry because I guarantee this will never happen. And for what it's worth the second stick was useless in 99% of PS1 games
And how exactly can you guarantee this?
By saying that most games which supported the Dual Shock controllers with analog sticks could also be controlled by means of the D-Pad since the base hardware was released without analog sticks at all. Control schemes were actually created for the D-Pad - the analog sticks either emulated the D-Pad input or had separate control schemes that only kicked in if the Dual Shock controller was detected.
Maybe I'm a bit slow today, but what you said seems to be completely unrelated to what I asked.
Second stick is useless in 99% of games ---> Actually, most games don't even require the two sticks as they work perfectly fine without them. ---> Automatically true.
Back then the sticks were added to facilitate gaming, they weren't meant to be an integral part of gameplay.