Let's say that you have a worksheet named Clients, with client names in A2:A100 and the corresponding email addresses in B2:B100.
On the sheet with the single command button, place an ActiveX list box with ListFillRange set to Clients!A2:A100 and LinkedCell set to A1.
In B1 on that sheet, enter the formula =IFERROR(VLOOKUP(A1,Clients!A2:B100,2,FALSE),"")
The code behind the single command button can be as shown above, but change the .To = "...." line to
.To = Range("B1").Value
This will set the to address to the email address corresponding to the selected client.