Remote Working
One of the Grey Knights lesser known powers is called Docupsyk (although some argue that its true name is Psykusign).
5 Prognosticars, 5 Librarians, 10 Purifiers, and 30 standard battle brothers gather around a great lectern servitor holding the offending document.
The ritual starts with the prognosticars delving deep into the warp, searching for the psychic presence of their long lost master.
Upon finding him, the Librarians open a small stable warp rift to him, supported by the minds of the battle brothers, while the Purifiers stand by to battle anything hostile that may emerge.
When Kaldor's hand emerges, a brother who has distinguished himself in his duties has the honour of placing a great gilded quill in his fingers, and guiding him to the place(s) he needs to sign. The whole ritual can take many days, and culminates in a five minute signing window.
This does mean Kaldor never gets to read what he's putting his name to though, and on the rare occasions he is met in full and in person, he expresses serious doubts as to this method, but it's the best option they've got.
Even in the depths of the warp, a Chapter Master will never be free of paperwork.