Since these tools trim using different approaches I don't think you can translate that command to fastp one to one. These approaches being quoting from the fastp paper:

fastp supports automatic adapter trimming for both single-end and paired-end Illumina data and uses different algorithms for each of these tasks. For single-end data, adapter sequences are detected by assembling the high-frequency read tails; for paired-end data, adapter sequences are detected by finding the overlap of each pair.

Given that Trimmomatic, Cutadapt and SOAPnuke are all based on adapter-sequence matching, ...

The fastp paper has benchmarks against Trimmomatic. I suggest you create a small test set and try out different parameters and see if they output your desired results. Here is a video demonstrating various fastp parameters.