Why is my LED less bright when activated through a vibration switch? How can I avoid this?
simulate this circuit &ndash; Schematic created using CircuitLab

This is the simplest solution that might work, depending on battery resistance.

As you have deduced the brightness is reduced because the LED is blinking on and off at a higher frequency than your eye can perceive. A capacitor in parallel with the LED will charge up while the switch is closed and power the LED briefly while the switch is open. Something in the region of 10 to 100 uF should suffice. The voltage rating of the capacitor just needs to be >= 5 V. You should really solder it in.

Aside: LEDs require current-limited power supplies. Usually a resistor is connected in series between the power supply and the LED. Since your LED is powered by measly button cells with a high internal resistance the current is limited by the battery. If you were to connect the LED directly onto a power-supply with constant 4.5 V it would probably die.