It is, without a doubt, the second option - that phrasing (or the Norse equivalent "ör í kné") is to the best of my knowledge never said in the Norse corpus. It doesn't match the image of marriage presented in the Norse sagas*: marriage is fundamentally transactional. While there is some evidence in a belief that marriages that do not have the consent of the bride would end poorly, legally speaking, marriage was a transaction between the father and the suitor. It was not something that would "trap" a man, or prevent him from doing things to earn his renown - it instead, if he married well, did precisely the opposite. The new family connection would increase his status and enable him to do more renown-winning things!

A wife was also supposed to manage the farm in Iceland and Norway while her husband was away, typically at a thing, or assembly, but also due to outlawry or a trading/raiding voyage. She would deal with hiring/firing, payment, the tending of the hayfields, and should it be necessary, the cutting of the hay. An unmarried man had to do all that himself, or hire a manager. This did give women a high degree of autonomy in certain aspects, and the more we look the farther that autonomy stretched, but it without a doubt gave men generally more autonomy to leave a single place. This is the precise opposite of the regretful, stationary role the guards in Skyrim have to take after their "arrow," which fits much more closely with the modern stereotype of the wandering bachelor "settling down" in one spot after marriage.

*The sagas are largely composed in the 13th and 14th centuries, a long long time after the end of the Viking Age, and in many respects, including specific dialogue, they are very bad representations of what the Vikings themselves did. However, much of the ideas in modern media about the Vikings are derived from these saga texts, making them appropriate to cite for your question.