This part: shiphandle:triggerAnimation("scripted", 0, true)
I'm assuming goes into scripting.tbl, somehow? Or can it be done directly with script-eval?
Complete scripting novice here - I've only ever used it for gravity and that's about it. 
Yes, you can use script-eval, and probably what you should do if you're not comfortable with scripting.
Use this as your scripting.tbl, or as whatever-sct.tbm, or just add everything except the first and last line to an existing file:
#Conditional Hooks
$Application: FS2_Open
$On Game Init: [
trigger_anim = function(shipname)
mn.Ships[shipname]:triggerAnimation("scripted", 0, true)
end
trigger_anim_reverse = function(shipname)
mn.Ships[shipname]:triggerAnimation("scripted", 0, false)
end
]
#End
Then, you can call those functions with script-eval like this:
( script-eval "trigger_anim('Alpha 1')" )
Yes, the argument to give is literally "trigger_anim('Alpha 1')". It's a bit of a hassle, since if you don't want to hardcode the ship name in every call, you'll have to concatenate the argument string from "trigger_anim('", the ship's name and "')". I'm sure you can also pass the boolean value as a second argument instead of defining two functions somehow, but I haven't tested that.