The overwhelming likelihood is that your request will be denied. Interlining is only intended for journeys booked in a single transaction.

Either book all travel on the same ticket (WS and KL have a relationship so this should be possible), or allow sufficient time between tickets to go landside, collect your luggage, get to the check-in for your next flight, and to get back airside through security before your next flight departs (bearing in mind that queues for security are extraordinarily long, and expected to remain so right throughout the winter. But perhaps "extraordinary" is no longer the correct adjective; it's been like this almost constantly since late April. See the long-running Mess in AMS today - April 2022 onwards thread)