The batch effect will be minimized (likely not eliminated, since there may be other subtle confounders!) if you use only read #1 of the PE dataset. Whether that actually makes any real difference will depend on the details of your dataset.
Most of the differences that you would see between SE and PE mapping are related to repetitive regions (assuming that both data sets have the same read length). PE reads can map inside of repetitive regions given that the other pair is in a unique region. Also, because PE has more information it can map sometimes inside repetitive elements.
Thus, if you want to make a fair comparison between SE and PE you should map one of the PE read mates from the start as Devon suggested.
However, if you plan to compare coverage of reads, you can simply extend the SE reads to match the expected fragment length and extend the PE reads to the fragment length. Also you should use a random mapping strategy for repetitive regions. You may have some small bias around repetitive regions but unless you are looking for something specific to repetitive regions you wont have to worry.