I am chiming in late, so ...

Running used to be my thing (and only thing) so in a Tri it is still my thing. I only run 3 days a week, swim 1, and bike 2. Every other week I will do a brick, either bike run or swim run. I average 1200 m/60 mile/18 miles a week respectively, and I race up to HIM distance.

If running is your fear, there is not much you can do in 4 weeks that will have a significant impact on performance. There is one mental thing you can do. I assume that the run is 5K? Pick a day next week, skip a day or 2 of running, then go out and run 3 or 3.5 miles. For you it would be the equivalent of a "long run." Then bike or swim for a few days afterwards to recover. It will not help your fitness, but it will help you mentally. It will prove you can do it (which I have no doubt you can) and it will introduce you to what that point of a run feels like.

Also, keep this in mind: If you can keep yourself under control in the swim and most of the bike, the adrenalin and atmosphere will get you through the run.

One more thing: If you have not done a "brick" then you are going to be surprised when you start running. I tell first timers to consider walking for 100 m or so before running. You might consider doing the same.

Good luck, you will do fine.

Mark