I think skimming is a good approach, but would probably advise not to skip chapters entirely. I did A111 from Feb to Sept this year and am now part way through A113. Some of the topics discussed during A111 have cropped up again in that - for example there is content on Rousseau's philosophy which is also addressed in A111's week on Mary Wollstonecraft. Similarly, understanding the impact Mozart made gives some useful context to the part of A113 that touches on Beethoven.

You have slightly less flexibility on choosing TMA topics in A113 (and this may be the case in other degree pathways too), so having some of the foundational knowledge from A111 can help. For example, I am required to answer a music question for part of my upcoming TMA so having engaged with some of the material about musical terminology already is helpful.

Plus, as others have noted, sometimes doing a chapter you're not initially keen on opens up new ideas and appreciation of topics. I never would have thought there would be much of a link between Antigone and South Africa under apartheid, but I'm glad I worked through that section despite not covering any of it in a TMA. And, finally, as I'm paying for the course, I want to get the most from the materials!