It is okay to change skips during a survey, but you need to consider the effects of that change.
Let us break the issue down in to 4 groups ...
1/ Respondents who have not started the survey.
They will see the new version of the survey.
2/ Respondents who have completed or disqualified from the survey.
Their data will not be affected at all. The data will represent the old version of the survey.
3/ Respondents who have started the survey, are incompletes and have not reached the question where the skip was changed.
These respondents will see the new version of the survey.
4/ Respondents who have started the survey, are incompletes and have passed he question where the skip was changed.
These respondents will have their data resemble the old version of the survey. One additional consideration here is where a respondent can click the back button (if you have it activated). They can go back to the point where the skip was changed. They will then see the new question and experience the new skip.
So consider all of the above and the different effects the skip change will have.
I have encountered this issue many times before, made the change, and finished up with data that looked just fine.
To boost your confidence, I recommend you start a couple of test surveys (one before the skip change and one after the skip change) and suspend them as incompletes. Make the change to the survey, then go back in and complete both test surveys. Then check the data to see what they look like.
Just one final point to review: Go and have a look at the incompletes and see how many surveys are hovering around the question/s where the skip is about to be made. It would be nice if the counts were low around the question/s where the skip change is being made.
And a further comment on changing MR questions to SR questions (or vice-versa), your data for these questions will change structure. So the most appropriate action to take here is to skip the old MR question always, and insert the new SR question that the respondents will now see. So you have some data appearing as the old MR question, and some data appearing as the new SR question. Your data stores both types and you can analyse as you see fit.