Is 筆順 a more professional sounding term?
1 Answer
IMHO, using 「[書]{か}き[順]{じゅん}」 does not sound childish per se. It is indeed in wide use across all age groups. It is when compared with 「[筆順]{ひつじゅん}」 that 「書き順」 could possibly sound slightly more informal, if not necessarily childish, but the difference is still fairly minimal.
The gap in formality and technicality between those two words is not as great as one might often expect to exist between an originally Japanese word and its Sino loanword counterpart. This is because 「書き順」 and 「筆順」 do not represent such a pair in that while the latter is a Sino loanword, the former is a hybrid, not a pure [大和言葉]{やまとことば} (with 書く being originally Japanese and 順 being a loanword).
I personally could not think of a situation where using one of these two words could sound considerably more formal, informal, adult-like or childish. If you have experienced such a situation, please do tell us.