Splitting HDMI (from RPi Zero) to HDMI+DVI

[analogix]

Using a Raspberry Pi Zero as part of an RGBtoHDMI setup for a vintage computer I was wondering if (and how) I could split its Mini-HDMI output into two connectors: HDMI and DVI.
That way I'll be free to attach for instance a TV (HDMI) or a slightly older monitor (DVI) without using any further adapters. The intention isn't to use both at once, but if that's possible (and I don't have to worry that something blows up in case I do attach something to both connectors at once) it's great.

Is it a simple matter of buying a cheap HDMI splitter (which I assume is passive and simply takes the single HDMI output and attaches two HDMI cables to it at once), or do I need some sort of active electronics? And which type of DVI connector would be appropriate to use here? DVI-D or DVI-I? I'm pretty sure it's "Single link" though.

PS: I know I could use a cheap HDMI to DVI adapter plug for this, but two dedicated connectors is more practical and elegant IMHO