I don't think there is no problem in the question, in so far as the Teacher नैयायिक, is capable of expressing himself and transferring his talent to his students, the media of instruction of little significance.
"श्लिष्टा क्रिया कस्यचिदात्मसंस्था संक्रान्तिरन्यस्य विशेषयुक्ता। यस्योभयं साधु स शिक्षकाणां धुरि प्रतिष्ठापयितव्य एव।।"
according to Kalidasa. The same, on the other side,
पात्रविशेषे न्यस्तं गुणान्तरं व्रजाति शिल्पमाधातुः ।
जलमिव समुद्रशुक्तौ मुक्ताफलतां पयोदस्य ॥
it depends on the capacity of the student to reflect whatever he receives from the teacher qualified as above. In both these cases combined, the language of instruction is guided by the teacher and the student both.
And the reverse, भवभूति exclaimed -\
वितरति गुरु: प्राज्ञे विद्यां यथैव तथा जडे न तु तयोः ज्ञाने वृद्धिं करोत्यपहन्ति वा |
भवति च पुन: भूयान् भेद: फलं प्रति तद् यथा प्रभवति शुचि: बिम्बग्राहे मणिः न् मृदां चय: ||
according to his scholastic view.
Now a days, as Panini has said, according to
"तदधीते तद्वेद"(॥ ४।२।५८)
one who is learning (अधीते) व्याकरण and one who already know (वेद), both would be called by the name वैयाकरण, so नैयायिक-s can be both who can read from translations and also who already have known inside and outside also would be called नैयायिक-s and both profess to teach in the language they can, as Sri Narasing Rao has already claimed.\
Hence I think there is no point in prolonging the discussion how the subject न्यायशास्त्र is to be taught using which media.
I remember, there was a general discussion about teaching Sanskrit through Sanskrit media some time ago. I don't know why this discussion about the subject in the language "Sanskrit" is concerned. Subject is different from the language in which the literature is available.
अवच्छेदक,अवच्छिन्न have their own concepts and theories behind them more than mere terminologies and without mastery over the concepts and theories behind them, practical usage of the terms may not be possible, in any language for the purpose of teaching as described in the beginning of this message.
The remaining is left to नैयायिक-s of the group.