What Antediluvian said about the IJN - other than the Kongo, there were a handful of coastal defence ships that were training ships by that stage, but the vast, vast majority of the IJN vessels that served in the 1936-46 period were home made. In terms of naval strength, Japan built 1.8 million tonnes of warships that are covered by HoI4 and served between 1936-46, compared with 1.6 million in Germany, 0.8 million in Italy, 0.5 in the USSR, 3.1 in the UK and 5.0 in the US (note that the US built 14.8 million tons of fighting vessels in total, and produced something like three times that of the UK, but if we just look at what HoI4 covers in discrete ships it's a lot closer), and these figures including vessels built before 1936 (as we're talking about Japan's industrial strength here, so pre-1936 counts as well) they look a lot closer to the UK in shipbuilding strength than they should).
From what I can see, on 1 Jan 1936, my best guess for what Japan should be building (not counting reconstructions because HoI4 probably doesn't, noting that for DDs and SSs the numbers are a bit of a guess, as I don't have the precise figures, but they should be close):
- 2-5 CVs (the variation is because one is a transport ship while under construction and two are seaplane carriers - so not covered by HoI4 - but were converted into the CVs Shoho, Chitose and Chiyoda after the game starts - I've no idea how HoI4 treats these).
- 2 CAs (Tone class)
- 2 'big' CLs in the Mogama class
- 11-15 or so DDs (10 Shiratsuyu class, 1-5 Asashio class, I don't have the exact dates for them on me)
- 6-7 SSs (1-2 KD6a class, 2 KD6b, 2 J3 class, 1 K5 class).
Just some numbers for perspective, apologies for any mistakes and not suggesting HoI4 has to hit naval production perfectly. Ten dockyards does seem a little low for this, but I remember looking up the same data for the UK and Germany, and Germany in particular had pretty low dockyard numbers for what it was building at the time (from memory, Germany was building more ships in terms of tonnage than the UK at game start, it was only in 1937 that the UK put the foot down and shot ahead on naval production).