I had two line managers until recently, because they job-shared, although one of them left a couple of weeks ago. Between them, they supervised all the office staff in our department, and I was answerable to whichever one of them was in at the time. But when it came to appraisals, they each had nominated staff to appraise.
You shouldn't be expected to have two appraisals - it would be one or the other, although your two line managers will maybe consult with one another over how they perceive your performance.
If I were you, I would have a quiet word with the line manager you feel most at ease with and tell them your worries. Chances are you won't have those worries for long.
No-one looks forward to staff appraisals, I think, but my last two have been very positive. I've had a very good manager who helps me to solve my problems rather than moaning about them. Now he's left, the task goes goes to his job-share partner, whom I get on very well with, but she doesn't have the same, easy management style as he does, and it might not be so pleasurable.