I ran into the exact same issue earlier this year. The best answer I found was here: thegreyblog.blogspot.com/2014/03/shrink-your-time-machine-backups-and.html In summary, Time Machine always creates a full backup, not an incremental backup. So, no you won't cause any harm by deleting the first one. I've done so with no adverse consequences. Second, use the tmutil command to remove old backups. sudo tumtil gives you the full list. I wrote a bash script from the command line, as the author suggests. I deleted everything I had from last year, starting with the first backup that was made in October, with:
$ sudo tmutil listbackups
Password:
/Volumes/Seagate Backup Plus Drive/Backups.backupdb/mkauffmanmbp/2016-01-01-003303
/Volumes/Seagate Backup Plus Drive/Backups.backupdb/mkauffmanmbp/2016-01-02-005714
There were a lot more lines, what we're after here is the location to use in the next line. In my case it's /Volumes/Seagate Backup Plus Drive/Backups.backupdb/mkauffmanmbp/ You will need to do the same, and use the \ before any spaces in the path as shown below. Below I used 2015-1* because mine started in October of 2015. So I had 2015-10, 11, and 12. If you want to get rid of all of 2015 you can use 2015-*. If you wanted to get rid of everything before October you could use 2015-0* which would remove 01,02,03,...09 of 2015.
$ sudo tmutil disable local
(The following is all one line.)
$ for i in /Volumes/Seagate\ Backup\ Plus\ Drive/Backups.backupdb/mkauffmanmbp/2015-1* ; do tmutil delete "$i" ; done
$ sudo tmutil enable local
Hope this helps!
Happy New Year!