The Green Clean
You are currently cleaning the beach mechanically. Considering the effects this might have on the local ecosystem, other options might be more fitting for your beach.
One of these options is cleaning manually. The best way to do this is to get volunteers involved. Organise clean-up events and maybe join a beach community. Make it fun for the volunteers so they keep coming back. When this is not an option, some cleaning companies don't only offer mechanical cleaning but manual cleaning too. This however does have a higher price tag as they will need a lot of labour to do this. The effect manual cleaning has on the environment is lower than mechanical cleaning, even though it is harder to pick out smaller waste like cigarettes.
Alternatives are to move the wrack that is present on the beach to the edges of the beach that are less frequently visited. This way the nutrients still stay at the beach, But the part that the tourists visit can be cleaned. In addition, more waste bins could be added, or the waste bins could be emptied more frequently. This way the chance of litter just being dumped on the beach is lower, reducing the cleaning costs.
Smoke-free zones could also be implemented. This way smoking is totally prohibited on the beach or smokers could have a designated area where they can smoke, like a terrace. preventing cigarettes from ending up on the beaches can already result in a lower need to clean manually.