Here is what solved it on my 98 SVT, and my brother's 95 Mystique (which was near impossible to open).....
The latch that connects with the door strike over time builds up surface rust and does not move freely. I moved the latch on the inside edge of my door using a screw driver and found it was very tight. I tested it by latching the assembly but with the door open. When I pulled the outside handle, I barely saw any movement. I had to click it over the rest of the way with the screw driver.
I added some general purpose lithium grease to all door latches and opened and closed the doors repeatedly. As the grease worked it's way in, all the doors opened easier and easier. I barely have to lift the outside handle on my doors now to get them to release.
I had replaced the latch assembly on my brother's Mystique with parts from my SVT parts car. It was good for a little while and started going back to how it was when we bought the car. That's when I found the grease solved it completely.
Try that before anything since it doesn't require removing any parts on the door.