Just my suggestions. It doesn't have to be emotionless, but he tends to speak more sophisticatedly. The voice here sounds more like Guybrush Threepwood or the guy from Broken Sword, for instance. It doesn't have to be devoid of emotion - for example, when he hears another Doctor has been in communication with K9, 'Interesting!' He tends to be philosophical: 'The thing about impressive doors is they are usually the gateway to something important'. Or uses a lot of jargon, due to his scientific knowledge 'It's a cyber-psudellian 6Y locking system. Where's your skeleton transverser when you need it?' Or he waxes lyrical about his journeys, 'More sticky than the jaws of an Alazarian arachnid.'..
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Oh absolutely, I agree with all of that.
I went back over the dialogue, the moment when K9 says that he was sent by another Doctor and the reply from the player Doctor is 'WHAT!?'....It's really just a play on the fact that the 10th Doctor has the whole 'what....WHAT........WHAT!?' catchphrase throughout his run.