As I understand it, you have 30 shape files each contains up to 250,000 points the points are planer (on a single plane with no elevation differences) and may be located so as to line up in certain ways.
You want a single polygon that encompass all the points in all the shape files
Well, the Minimum Bounding Geometry (Data Management) tool will generate bounding polygons for features or groups of features. I suggest you are interested in the Convex Hull option.
You could run Minimum Bounding Geometry with the Convex Hull option on each shape file and then either Union all the output hulls or merge all the output hulls and run Minimum Bounding Geometry on that merged data set.
You may want to set up a python script (or a model-builder model) to loop through all your 30 inputs and to handle the 30 outputs. If the shape files have that many features you likely don't want to make just one honking big merged shapefile of 7,500,000 points (250,000 x 30) to run the tool on, so working on each input by itself should work better...