I had some time over the weekend to play a bit with Tiny Core Linux.
Tiny Core Linux is (IMHO) the only (or maybe one of very few) Linux distros that makes sense outside a "full", "normal" install, where you have to decide between 23 text editors, 3 or 4 shells/GUI's, etc. in a multi-Gbyte install, as it is highly modular.
Of course the way this modularity has beem reached is highly debatable, and if you want something the way you like it it is a PITA to put together something working.
Anyway, a 150 Mb image can contain the Linux system with GUI (around 30 Mb), a netinstall and a (mipsbe) .npk (around 70 Mb including the netinstall .tar.gz) leaving 50 Mb free/usable, the "extra" .npk still mipsbe is another 15 Mb zip.
So the "final" version should probably be around 200 Mb, to leave even more free space available and be on the safe side.
I went for the 9.0 version (current is 16.1) because it seems like the last one that includes in the on demand install repository the QtWeb browser (which is lightweight and good enough to access https://mikrotik.com/download), the only meaningful alternative for more recent versions is dillo (which I don't particularly like).
I also tested the CLI Lynx browser, and it works to download from Mikrotik just fine, but probably it won't be much appreciated by non-Linux guys, anyway for the CLI/text only version one could use MC (midnight commander) instead of xfe as file manager, personally I am very fond of OFM's (orthodox file manager).
Anyway, packages to download and install are:
tc-install-GUI <- to create the image from the booted .iso
Qtweb <- web browser
Openssl <- otherwise there would be issues with https certificates
xfe <- file manager (the only one that seems like working good enough while still tiny and including expanding/extracting capabilities for both .tar.gz and .zip )
Then you can access Mikrotik and download the netinstall and the needed .npk's.
I tested that netinstall starts just fine in this test (Virtualbox) VM (in the sense that it runs and gets to the "waiting for routerboard"), but I have had no time/will to attempt actually netinstalling (needlessly) a Mikrotik device, I will try next time I have a serious issue with a device.
However, loosely - though probably some touch-ups will be needed - 200 Mb seem like more than enough.