Your logic escapes me, but let's not worry about that right now. I'm a pragmatist. I mostly care about getting it working.
You can try that relay in that circuit as is, try reducing the capacitors to 68 uf, try a 9 volt battery because it has twice the voltage as the relay rating, and add a 680 uf capacitor from +9V to ground to supply the current surge that a 9V battery can't do very well...in that order.
You can try that relay in that circuit as is, try reducing the capacitors to 68 uf, try a 9 volt battery because it has twice the voltage as the relay rating, and add a 680 uf capacitor from +9V to ground to supply the current surge that a 9V battery can't do very well...in that order.