You can generate a bulk download of your shipping labels on Postmen.
This will merge all your labels in a single PDF file which can be downloaded and printed at a go.
You can create a bulk download via API https://docs.postmen.com/api.html#bulk-downloads-create-a-bulk-download
By going to Postmen -> Explorer -> Create a Bulk Download -> Enter the label ID's in the Body which you would like to bulk download and then click on Submit.
In the Response you will receive a link to the pdf file.
You can download this pdf file and print. This will print all the labels at a go.