DNA-based data storage emerged in this decade as a promising solution for long data durability, low power consumption, and high density. However, such technology has not yet reached a good maturity level, requiring many investigations to improve the information encoding and decoding processes. Simulations can be key to overcoming the time and the cost burdens of the many experiments imposed by thorough design space explorations. In response to this, we have developed a DNA storage simulator (DNAssim) that allows simulating the different steps in the DNA storage pipeline using a proprietary software infrastructure written in Python/C language. Among the many operations performed by the tool, the edit distance calculation used during clustering operations has been identified as the most computationally intensive task in software, thus calling for hardware acceleration. In this work, we demonstrate the integration in the DNAssim framework of a dedicated FPGA hardware accelerator based on the Xilinx VC707 evaluation kit to boost edit distance calculations by up to 11 times with respect to a pure software approach. This materializes in a clustering simulation latency reduction of up to 5.5 times and paves the way for future scale-out DNA storage simulation platforms.