I think it'd be moderately easy to give yourself a little time before diseases hit.
1. Alter the 'give self disease' interactions to be useable only after ~1200 ticks, and give them [IT_CANNOT_HAVE_SYNCLASS:NOT_DISEASE_AFFECTABLE].
2. Add to all dwarves a 'give self immunity' interaction that's useable immediately and temporarily gives the synclass NOT_DISEASE_AFFECTABLE. Give it a wait period that's quite a bit longer than the time it lasts for. Give it [IT_CANNOT_HAVE_SYNCLASS:DISEASE_AFFECTABLE].
3. Add to all dwarves a 'give self vulnerability' interaction that becomes useable just before the 'give self immunity' interaction ends, and permanently give the synclass DISEASE_AFFECTABLE.
Let's make the 'give self immunity' interaction last for one year. What should happen is the following:
1. Dwarf pops on map.
'Give self disease': not useable
'Give self immunity': useable
'Give self vulnerability': not useable
So they use the immunity interaction. Shortly after that, the disease interaction becomes useable, but is blocked by the synclass given by the immunity interaction.
2. Dwarf has been on the map for eleven months.
'Give self disease': useable, but blocked by immunity.
'Give self immunity': useable, but still in wait period
'Give self vulnerability': useable
So they use the vulnerability interaction*. Shortly after that, the immunity interaction finishes its wait period, but is blocked by the synclass given by the vulnerability interaction.
3. Dwarf has been on the map for twelve months.
'Give self disease': useable
'Give self immunity': useable, but blocked by vulnerability.
'Give self vulnerability': useable*
So they use the disease interaction, if they have it.
This means that all dwarves will be healthy for one year after they appear. It's probably possible to make it so that a dwarf who's been on the map long enough sends out something to block the immunity interaction on any newly-arriving dwarf, but I haven't quite worked that one out yet. What I'd really like is a way of making at least the starting seven permanently immune, without having every dwarf to appear having that same immunity. Could maybe be done by making the diseases triggered by other creatures using a syndrome not immediately useable, with the delay allowing the starting seven time to put up immunity.
*And keep spamming it, since I left out the [IT_CANNOT_TARGET_IF_ALREADY_AFFECTED] to prevent capslock fatigue.