RAND cells but ignore empty cells with data at the top

I am trying to create a random draw for a golf team event with teams of three, where each team consists of a low - mid - high handicap player. Now I have created the the total number of players under one tab where I sort them into handicap order low to high; then selecting the lowest third I copy and paste them into the low handicap group under tab Random in the sheet below, repeating for the mid and then the high.

In the Random sheet I have created a macro worksheet where I am trying to do a randomized draw. I have three columns with adjacent RAND columns alongside each. These are columns A - H respectively. There are 23 rows with the heading in row 1. Now after pasting the above entries as above via a button that activates a macro to paste the data into the relevant column.

Once I have all three columns occupied I then run a macro called RandomDraw which randomizes all three columns. Problem is the data is sorted in all three columns but it sorts the blank cells as well. How can I make ignore the blanks and leave the cells containing data at the top. In this instance I only have 8 names in each column but this could vary.

The macro that does this is as follows.

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Sorry about that but I did not realise this. Hope this OK, I am a relative newbie.