Some smart ways of streamlining the OHSMS is to systematically work through the standard. If you are not using a toolkit that guides you through the implementation, then it is best to go through the ISO 45001 standard in order from clause 4 through 10 as it is in a fairly good order to understand the OHSMS. The only thing that is out of place is that you will want to set the process for documentation control (clause 7.5) first so that you have the rules for recording procedures and records as you go through.
The other thing to keep in mind is to think about what you already have in place that could meet the requirements of the standard as you work your way though. If you are meeting your OH&S legal requirements you will likely have many processes already in place that might either completely, or partially, meet the standard requirements. It is also helpful to ensure that you think about what documentation you actually need instead of just trying to document everything. Simple and concise documentation will be more helpful that complicated and confusing procedures.