From what you state, using Trimmomatic in Galaxy should be ok with the "Nextera (paired-ended)" built-in adaptors. But you can test it out and use customize adaptors (if needed) using the same tool form.
Run FastQC on the data before and after to review the trimming results (test to see if the adaptor was actually clipped correctly).
The functions in the Galaxy wrapper mirror those in the command-line version of Trimmomatic. Their manual covers usage/formatting that applies to both. See the section "The Adapter Fasta" here http://www.usadellab.org/cms/?page=trimmomatic
Thanks! Jen, Galaxy team