First I think you have understood the sentence correctly. Your question is one that can be (and has been) answered very briefly if we assume you understand certain dynamics of Japanese grammar. Unfortunately explaining the dynamics takes a bit longer but this is my attempt:
1) When a sentence ends with a phrase such as 心配なく I would say there is an "elipsis" or unspoken phrase that is so clear it does not need to be said and, as a result, the phrase has become a set expression in itself. There are many cases of this in Japanese. For example 電車に乗らなくちゃ (I have to catch the train) is an abbreviation of 電車に乗らなくちゃいけない (ちゃ=ては)）
2) なく is normally found in the middle of a sentence and introduces a pause (almost "mini-climax") before finishing with a definite statement (punchline?) such as the following example:
外国へ行くとしたら、ただの旅行ではなく、勉強を 目的として 行きたい。
If I ever go abroad, I don't want to travel for just pleasure, I would like to go to study.
When a sentence ends in 心配なく the speaker is typically saying something along the lines of "Don't worry...(it'll be alright, there is no problem)" or "Don't worry...(it'll be alright for the reasons just discussed). eg
don't worry, there is no problem
We also see this in polite set phrases:
Please don't wait, start eating
3) Before looking at your sentence it might be helpful remember that in spoken Japanese phrases are often given in reverse order, possibly because the speaker wants to communicate key words first eg 「僕は行かない」 might become 「行かない、僕は」.
In your sentence it should be easy to see there is no need to add anything to the existing sentence because the important matters have already been said and if we reverse the order we get:
"At first you might not be able to control Link but you should not worry because you will soon get the hang of it"
In your comment you ask about honorifics. As you can see from your example sentence, I would say they are not required in casual conversation but the point you raise is also illustrated in polite set phrases, when they certainly should be used. Possibly a native speaker might clarify this for us but in context of your sentence, if I wanted to be less casual it might be sufficient to deliver the sentence in the "normal order", ending the sentence with です.