Looking at the different Arcanoi descriptions, I think that the best option is to completely ignore the Angst gain for Spectres. Here's why:
Arcanoi that cause a Wraith to gain Angst do so with the understanding that the Wraith is taking an action that helps to fuel Oblivion. The worse the act is, the more Angst the wraith gains. For example Muse (Keening 3) is about manipulating another Wraith's subconscious. It gives one point of Angst. Rend (Moliate 4) directly damages another Wraith's corpus. It also gives a point of Angst. Obliviate (Outrage 5) sends something directly to Oblivion. It gives two points of Angst. The idea behind these powers is that they are so evil, their very use strengthens either the wraith's Shadow/Oblivion itself.
I'm going to assume that, for any given Arcanoi, that a Spectre will pay the Pathos cost with Angst, as Angst/Pathos seem to be two sides of the same coin. Let's hypothetically put a house rule in place that says "Each time a Spectre uses one of these powers, they must pay any the listed Angst as an additional cost, instead of gaining it, like a regular Wraith would." Obliviate (Outrage 5) is going to cost 5 Angst to use, 3 that replaces the Pathos and the additional 2 that are listed. 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, servants of Oblivion, to damage other Wraiths and to contribute to Oblivion. There doesn't seem to be anything in the flavor to suggest that Spectres need more of their personal power to activate the same effects as the non-Oblivion-tainted. As a rules change, that would seem to needlessly handicap Spectres.
Lets look at subtracting the normal Angst gain from an Arcanoi from the cost of the power. In this case, since we're fueling our powers with Angst already, we'd get a discount from the total cost of the power. While this does make sense, I would be hesitant to house rule this for balance reasons. Looking back at the example Arcanoi, Obliviate would only cost 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 for a regular Wraith would cost next to nothing for them. But their Dark Arcanoi would actually require MORE Angst to use than a power of a corresponding rank.
If we look at gaining Composure instead of gaining Angst, there is some 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, it seems like 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.) But, as you point out in the question, it definitely doesn't make sense for a Spectre's good side to become more powerful if they're destroying something with a power like Obliviate. This option is definitely out.
(Side note: It might be good to house rule some of the regular Arcanoi to give Serenity as well, when used by a Spectre. Almost all of the Castigate powers would be good candidates for this.)
I think that ignoring the Angst cost 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.