Itachi knew of the izanami and he considered Shisui as his brother so it is possible that he shared the information with shisui? while kotoamatsukami requires time before it can be used again, izanami is a one time use of the eye so Shisui could have avoided using it. I know that the answers will just be extrapolation only but still might be worth asking
The short concise answer:
If Shisui knew about Izanami, then yes he can use it. If not, he can easily learn it by reading the Uchiha stone tablet with his Mangekyou Sharingan.
Considering all events leading up to his death, he probably never learned about Izami (reasoning below).
The nice long juicy explanation:
Because the Uchiha had a past history where people started abusing the Izanagi and Izanami, they became labeled as kinjutsu or forbidden techniques. Kinjutsu is not taught to shinobi on a general basis.
That means one can only learn of Izanami either through the stone tablet or another Uchiha that knows how to use this technique. From what it appears, Shisui had considerably the best pair of eyes amongst the Uchiha clan. With that said, Shisui is definitely capable of using Izanami as so should any other Uchiha member that awakens their mangekyou.
However, it only makes sense that Shisui did not know about Izanami before the Uchiha coup d'etat. Recall Shisui trying to use his special technique Kotoamatsukami on Danzou prior to the event. If he knew about Izanami, I am sure he would have used it, because it only requires the eye sacrifice, which is better than having Danzou stealing his eye.
In order to protect his last eye, Shisui sacrifices his life and entrusts his eye to Itachi. Therefore we can determine that Shisui did not know of Izanami.
EDIT: Addressing R.J's comments - (This really doesn't add to the answer of the titled question, but explains the fundamentals of Izanagi / Izanami).
I think any Uchiha can use Izanami or Izanagi provided they know about the jutsu.
Anyone (not just Uchiha) can use Izanagi / Izanami provided that they know about it and have a Sharingan (ie Danzou).
There is no pre-condition of them having awakened the Mangekyou because if that was the case, then Danzo couldn't have used it so many times.
For a person to use Mangekyou techniques in the past (amaterasu, tsukiyomi, susanoo), it required him to use his Mangekyou Sharingan. The only other type of eye that can use the above 3 jutsus is the Rinnegan, and that is because it is the evolved form of the Mangekyou.
When Danzou used Izanagi 10 times, 10 normal sharingan were sacrificed. This means that Izanagi is not a Mangekyou technique, and does not require Mangekyou to use.
All you need is an activated Sharingan and the knowledge about the jutsu.
Before I begin, we know that you also need Senju DNA in order to use Izanagi. This was explicitly stated by Tobi when Danzou was fighting against Sasuke.
In Danzou's situation, we can assume that Danzou needed the Mangekyou Sharingan in order to learn about the technique. Who is going to teach Danzou Izanagi? The possible options are Madara, Obito, Shisui, and Itachi, except none of these people have motive to teach him Izanagi. Therefore it is only logical to assume that he needed to read Uchiha stone tablet with MS.
The possible plot hole:
Tobi stated that you need both Sharingan and Senju DNA to use Izanagi. Keep in mind that both Tobi and Danzou had both DNA when using that jutsu. Naturally, I'd assume the same prerequisites hold true for Izanami, however it was never mentioned that Itachi has Senju DNA. That means Izanami and Izanagi have different requirements, or Itachi has some Senju DNA, or this is one big plothole mess.