I suggest to review your board , do both boards have fine pitch QFP's or TSSOP's? . If yes, best approach is to finish board at a time to ensure best quality . You can refer to your solder paste TDS to justify why you choose this approach. If one of the board dont have fine pitch you can do manual print. You can use PCB break away as stopper . One operator do the squeege action, while other secure the alignment by holding the stencil frame ,old school but effective. If this is not allowed, you can design simple manual printer using simple backyard tools like C clamp and bearing. When I was in the manufacturing,I made one and proven to be effective .
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