Yes, rather like that! A small one, that he can easily carry in his satchel.
Projecting words by magical means instead of using a muggle device would be perfectly acceptable, yes.
I expect you think I am being a stubborn and difficult man, when you are offering a great service. I need you to understand something. If I were to knowingly allow you to use computers and other muggle machines to examine my blood and to do this work, it would be most severely injurious to my good name, and to Siri's. I do not think that I can hold notions of personal honour higher than that dear child's life, so I will tell you that you must do what is necessary to create your potion to save him. You will have my word. You will have my agreement. I am setting aside tradition and proper procedure for his sake, and asking that you do the same, and come to a private and undocumented arrangement with me. The very thought of giving up my blood is a daunting and disturbing one, and I am sure you understand why. I am asking you to make this business safer for me, and for him, by leaving no trace of a record behind. I know that I cannot force the matter, but I hope to have your understanding, and your agreement.