Looking at the different Arcanoi descriptions, I think that the best option is to completely ignore the Angst gain for Spectres. Here's why.
The Arcanoi that cause a wraith to gain Angst do so with the understanding that the wraith is doing something that fuels Oblivion. The worse the act, the more Angst gained. For example Muse (Keening 3) is about manipulating another Wraith's subconscious and gives one point of Angst. Rend (Moliate 4) directly damages another Wraith's corpus and also gives a point of Angst. Obliviate (Outrage 5) sends something directly to Oblivion and grants two points of Angst. The idea behind these powers is that they are so evil, their very use strengthens either the wraith's Shadow or Oblivion itself.
Let's hypothetically put a house rule in place that says "Each time a Spectre uses one of these powers, they must pay Angst instead of gaining it." Also note that we are assuming that any Pathos cost for the power will be paid using Angst. Obliviate (Outrage 5) is going to cost 5 Angst to use. (3 to replace the Pathos and an additional 2) That seems rather steep, but it is a very powerful and Oblivion-fueling power. Rend (Moliate 4), in a similar fashion, now costs 2 Angst. And so on.
The problem that we run into here is that it's now more difficult for our Spectres (who are servants of Oblivion) to damage other Wraiths and to actually contribute to Oblivion. It doesn't make a lot of sense to say that they need to use more of their personal power to have the same effects as someone who is not Oblivion-tainted. It seems like a way to needlessly handicap them.
That leads us to the second idea, that we would subtract the Angst gain from the cost of the power. While this does make a lot of sense, I would be hesitant to do it for balance reasons. Looking back at the example Arcanoi, Obliviate would only be a single Angst to use, while Rend would be completely free. If you compare these to the Dark Arcanoi in Dark Reflections: Spectres you can see that the Angst costs are generally in line with the regular Arcanoi. Typically, a four or fifth tier power will cost one or two points of Angst.
If we used this option, Spectres would seem to be the masters of the regular Arcanoi. They could use them much more frequently than regular wraiths. Things that require a lot of power to use would be next to nothing for them. At the same time, Dark Arcanoi would still require them to use their own Angst, in most cases at a higher level than the regular Arcanoi.
As for the third option, gaining Composure instead of Angst, there is precedence for it. In DR: Spectres, the Larceny powers Withstand Oblivion (Larceny 4) and Defy Oblivion (Larceny 5) give an additional one and two Composure points, respectively. In this case, though, the flavor is that by trying to fight back Oblivion, the Spectre is feeding it's positive side. (Note that these powers each cost 2 Angst as well, so the Spectre still has to use some of it's own private power stash.) In fact, it might be good to house rule some of the regular Arcanoi to give Serenity as well. (Castigate, I'm looking at you!)
I think the fourth option makes the most sense. We're not making it harder for Spectres to do things that normal Wraiths can. A normal Wraith gains Angst by feeding it's dark side, while a Spectre is ALL dark side. A Spectre using an Angst gaining ability isn't paying more or getting a discount, it's just not enough to corrupt them more.
It seems like ignoring the Angst cost makes the most sense. It shouldn't be harder for Spectres to damage other wraiths/feed Oblivion. While giving the Angst cost as a discount makes sense, that may make Spectres too powerful. Composure is not a good option to replace it because the rules are pretty clear that fighting against Oblivion gives Spectres Composure and the powers in question are definitely not doing that.