Pipsqueak - we went end of April/early May, no midge problems - we've also been to mull twice during the May half term holiday and that was fine too.
Others may have more expert advice, but i think there's a couple of different ways to do it.
What we did was drive to Oban, stayed overnight there then ferry to Barra, at the southern end. This is linked by a causeway to Vatersay, a small island with a stunning 'tombolo' pair of beaches. We stayed a couple of nights. If you go to Barra, it's worth seeing it's airport in action (the only scheduled airline where the schedule depends on the tide!) and do book the Kisimul Cafe ... if the idea of an Indian restaurant on a Scottish island sounds unlikely, think again.
Then ferry to Eriskay, and then we drove up to North Uist via South Uist and Benbecula - these are all linked by causeways. We stayed 3 nights in North Uist. The coast round the top of north Uist is particularly fine.
Then ferry to Harris and Lewis - which is actually one island. Harris has the most spectacular combination of scenery, beaches and mountains - and eagles. Lewis has some interesting ancient sites along its west coast, in particular the broch. We had 3 nights in Harris, 2 in Lewis.
And then we took the ferry to Skye for a few nights... but could have instead got a ferry to Ullapool on the mainland.
If you wanted to just stay in one place, I'd choose Harris, if two then I'd combine Harris and north Uist.
The ferries are all Caledonian McBrane.