Travel / FROM Katowice-Pyrzovice Airport TO Krakow Balice Airport [7]

Hello everybody!

Could you help me with one issue..

Planning trip through Poland, and need to change airports in Krakow - arriving in Katovice Airport, departing from Krakow Airport.
Looking to rent-a-car to go between airports.
I have read few articles and forum posts, that there are road-works on A-4 way, is here anybody who drive it short time ago?
Is there traffic-jams on evenings?
I'm arriving on 20:50 in Katowice, and next flight 23:40 from Krakow, so i should within 1-1,5hours come from Katovice airport to Krakow airport. Is it real? Any advices about road?

As I understood, i'm going by S1 road, than change to A-4 and going by it to Balice.
Is it direct connected - Katowice airport to S1? Exit from A-4 to Krakow Balice Airport?
Any difficulties on road what i should clear? It will be evening time, and i try to minimize time from airport to airport.

Thank you VERY MUCH for reply!

best regards,
Viitaliy.