I don't want the Angels to empty their already barren farm, but they have a few extraneous pieces. I wouldn't trade any pitching prospect that has value, but here are some position players that have actual value:
1B - Cron
2B - Lindsey, Yarbrough
3B - Cowart, Jimenez
SS - Stamets, Rondon
OF - Calhoun, Grichuk
There are a few others - like Borenstein, Long, etc, but they don't have the value (yet) that the above do.
The Angels don't need Cron and I don't think he'll be any better than Trumbo, so he's available (or the Angels could wait a year and trade Trumbo and keep Cron).
Either Lindsey or Yarbrough will replace Howie Kendrick in 2016; so you only really need one. Rondon seems to have a lot of upside so I'd like to see him kept, but Stamets is tradeable. The Angels seem to have no confidence in Jimenez, so he's tradeable (although doesn't have much value). And then you have Calhoun and Grichuk, both of whom are extraneous. I'd really like to keep Calhoun and see him as the 4th outfielder.
So in my view you can trade Cron, either Lindsey or Yarbrough, Stamets, Jimenez and Grichuk and not really damage the future. I suppose your biggest concern would be trading the wrong one of Lindsey or Yarbrough, but none of the rest seem like they have star potential.