Caution if you use a capacitor across the TL431. We've found that certain brands (can't remember which) will oscillate when they have a capacitor across them. Any noise from the TL431 is going to be well under an LSB (10/12bit).
Also, if you follow Mikes suggestion - definatley don't put a capacitor across the TL431 - it will slow up your reference and require more power. Also, while the datasheet specifies 1mA through a typical TL431 - they will work well with lower currents. YMMV.
If the datasheet specifies 1 mA minimum current, they need 1 mA minimum current and will NOT work under 1 mA. They may, but as well may not. It is stupid idea to build designs like this, when there are legitimate low current "431" based references, that operate well under 100 uA.
Stability regions with parallel capacitive loads are also defined in every datasheet. No need to "find certain brands" by experimenting.
Disagree that it's "stupid" - low current 431's are rarer, more expensive - the NCP431 (Farnell: 2534159) is around $0.10 in 100's, a generic 431 is around $0.014 (LCSC: C181103).
Whilst low current 431's can be made to use 40uA, the dutycycle required in the OP's use case is likely to be so low that it's contribution to overall current consumption of even a 1mA TL431 would be measured in a few nA. The 100nF suggested is very much in the non-stable zone (ti datasheet: SLVS543P, fig18), 4.7nF or less, or 10uF or more. But I would argue that it isn't necessary with 10/12 bit converters.
I wasn't suggesting that someone tries different brands of TL431 - what circuit might work with brand of TL431 might not work with another - I have very real experience with this.