It is quite simple.
At turn-on, voltage divides as inverse of capacity. The "small" cap gets the bigger voltage.
After a long wait (maybe only seconds in audio), the voltage divides as inverse of leakage. The cap with less leakage gets the bigger voltage.
For two caps with "similar" insulators, leakage increases with uFd. 1uFd likely leaks around 10X more than 0.1uFd. If that is exactly true (never happens) then the initial and final voltage divisions are the same.
See below. Proposed plan in SPICE. 1uFd (notionally 600V rated) and 0.1uFd (notionally a 200V job). A 600V battery is abruptly connected at 1 mSecond, we watch for 100mS.
SPICE complains about the "floating node" at the cap junction. It can't compute a "DC" value here. Inspection shows there is no true DC value. But all caps leak. I have used arbitrary small and equal "leakage" resistors to shut-up the sim and to show what would happen over time.
At bang-on, the smaller cap gets 545V of the 600V, just 10/11. The large cap gets 1/11. As predicted.
Since the intent is to use a 200V cap as the "smaller cap", and it is going to 10/11 or 91% of the applied voltage, it is still going to pop at turn-on.
(Yes, 300V might be more usual. But that still comes to 272V, over the 200V rating.)
If the leakages were in-proportion to the capacitances, the lines would be horizontal (I did run this, boring).
Assuming leakage roughly proportional to C, the small cap always has the higher voltage.
A slower start changes things so slightly that it is no practical help.
I tried some tricks, like shorting the small cap until the large cap is full-charged. Yes, the small cap starts from zero VDC but will rise according to leakage, and the technique is awkward. Adding leakage (shunt resistor) does change the long-term VDC but does not affect the initial spike, and useful values are likely to mess-up the tuning you are doing.
A "200V" cap does not blow-up at 200.1V. There is a safety margin because there are weak spots to allow for. But in this kind of abuse, what can happen is the repetitive over-voltage surges burn-out uFd. Your "0.1u" cap becomes 0.09u, then 0.06u, etc. You won't know what you are really getting.
_I_ think the answer is to get/make a 400V-600V cap box.
Cap Assortment on Amazon has thirty 630V caps from 10nF to 1uF, and twentyfive 400V caps to 2uFd, for $12 free shipping (eventually). Series-parallel the extras of each value to get in-between values. ---Uhh, this may not be the best-bet vendor. 100% feedback, but only 9 of them, one "Perfect to my dog!". Ah, a fair assortment of assorted electronics, but the top product is a dog-leash.