On Tuesday it should be easy enough to reach Tighnabruaich – even starting in the afternoon – because it's only 10 km. That still leaves you a considerable challenge to complete the rest of the Way in only three walking days (Wednesday to Friday) and unless you intend to jog most of it I'd suggest you need a rethink.
Although the distances look modest on paper, the combination of steepness and terrain makes average speed slow, Cowal is very remote and there is little enough accommodation choice even if you overnight at the suggested stopovers (which are for a five-day walk, whereas you are attempting it in 3.5).
When you read the guidebook you will see various options suggested, one being via Wemyss Bay and Bute, but unless you are into challenge hiking/jogging using a headtorch and very long hours, I don't think rolling two days' walking into one will work on this route (except for the first two sections, but you'd need to start early morning, not mid-afternoon, for that). At least in September you should have 12 hours daylight but your question about "pickup and drop-off services from the airport to the first accommodation" suggests that you don't realise what a wonderful wilderness experience you are heading for.
If you haven't already read pp 5-9 of our guidebook, please visit this page
Planning (extract) and look carefully at the altitude profile and also the distance table. Food for thought?
