Yes, all spells cost gold to learn.
Copying a Spell into the Book
When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a level for which you have spell slots and if you can spare the time to decipher and copy it.
For each level of the spell, the process takes 2 hours and costs 50gp. The costs represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can prepare the spell just like your other spells.
That's a fixed cost - it doesn't matter whether the spell has a material component, no material component, or even an expensive material component. All spells cost 50 gp x spell level to learn.
I say to your players, something else is the way to go. Fake it til you make it. Give 'em the old razzle dazzle. Sell the sizzle.
You can't speak orcish, but maybe you can fake it with the best of 'em. Whatever the orcs say, nod, shrug, moan, make a vaguely orcish grunt, point to your mouth and move on. Or maybe when an orc says something to you, nod, try to make a sound that sounds like a sound the orc just made, and keep moving.
Some props might help. Wrap a bloody bandage around your lower face, and fake an orc with a ogre-size toothache. Maybe some real orc blood will help sell the smell. Maybe drag a "dead" halfling along like you're taking the body to the boss.
A little charisma and maybe some proficiency in performance and deception and some luck is your best bet. Any other spells you got, use 'em -- suggestion, charm person, friends, enhance ability, could all be useful.
A distraction might help. Illusory elves attacking on the other side of camp maybe. Elves, man, orcs hate 'em. Or maybe an ally lobbing a fire arrow into the other side of camp might cause a distraction. Setting fire to the tents is always an option worth considering.
And when the jig is up, and they're getting wiggy on you, you can point in the distance, wide-eyed, make some orcish grunts, and heel-and-toe it out the door. Haste might be helpful.
Best Answer
What makes the most sense to you?
The rules text doesn't make it at all clear exactly what that money is going to. There are three different options that I see: training materials, paying the instructor, or both. Depending on how you and your group sees it, any of those three options are totally acceptable. You should figure out which one makes the most sense to you, and stick with that ruling.
If the cost of training is just for materials, then you should pay full price. If it's just for paying the instructor, then you shouldn't pay anything. If it covers both, then you should pay a lesser amount, perhaps half.
The important thing to remember here (and elsewhere in 5e) is that when the rules are super vague like this, the best thing to do is figure out what makes the most sense for your group, and stick with that.