Shifting capacitors for 555 timer

Hi i would be really grateful if anyone can help me with this question.
I am working on a project but really stuck right now.
So i am trying to switch to the next capacitor after a certain time interval for the attached circuit.
I tried to use a 595 shift register but didnt work out.
Are there any other components or any methods that can enable this switching?

So basically the C1 will be the only connected capacitor for 10 seconds, and then C2 will become the only connected capacitor for 10 seconds, and so on.

For example: CD4051 analog multiplexer:

CD405x Analog Multiplexer

That's not how to switch them. Switch the low side of each capacitor to ground, much much easier, any NPN
or n-channel FET could do that. Yes an analog switch/multiplexer will also work, but watch out for
the high on-resistance of some analog switches.

Don't use Darlingtons to switch to ground, they have too high a saturation voltage.

The 595 cannot work because it has totem pole outputs, so it could only switch to ground or to +5,
not leave a pin open circuit (unless they all are, using the OE pin).

You could use Arduino pins, by switching them with pinMode from INPUT to OUTPUT. Arduino pin
drivers have about 40 ohms on-resistance, which compares favorable with some analog multplexers.

If you arrange the capacitance values as powers of two you can get 2^n-1 capacitance values from
n capacitors.

But why use a 555 in the first place? An Arduino can replace it all together... No 555 nor caps needed...

Are you using 555 timer to generate a signal? - If Yes you can simply remove it and use any of Arduino Pin and Timer to toggle pin as per your need.

Now as you want the input pin to select different capacitor time by time you can choose any Multiplexer chip for example SN74CBTLV3257 may work for you there are many other multiplexer chips available in market.