If you want to bet on the Southampton vs Manchester United match, then you can still consider a draw or Manchester United winning over Southampton. Manchester United's winning probability is quite convincing in my opinion, but you can bet on a draw if you don't believe in the away team's chances of winning. I have confidence in Manchester United to win that match, it's good to just have fun.
Although, when it comes to placing a bet between Manchester United and any other team they will play with regardless of the team performance, I always find it difficult to do because Manchester City performance sometimes is kind of surprising the way you think it may not go like that. And sometimes it will even go beyond your expectations. However, as for this match, I would rather place the bet on a draw and not Manchester United to win. I can't confidently give them a winning chance because of the result they had in their last matches.
Ten Hag will try to win the full 3 points in this away match following two previous defeats against Liverpool and Brighton. There is no reason for Ten Hag to remain silent on the sidelines and watch his team get beaten by a bottom team like Southampton, if he did then it would really be a shame for Ten Hag. He must find a definite solution so he can go home with a maximum of 3 points, including finding the right lineup and strategy.
Sure, Southampton is in the 19th spot in the table, so if Manchester United lose this match, then seriously, it will be a shameful thing for them, as you said, and also, it will be too bad to lose 3 matches when the season just gets started. I hope Manchester United will do everything in their power to secure the 3 points you said so they can move forward in the table too.