There is no way to reformat a hard drive to a completely different format type and have it non-destructive.
That's not true; Microsoft actually includes a FAT to NTFS converter in Windows, and has at least as far back as Win2K. Way back when HFS+ first came out there was also a commercial Mac app that could convert an HFS (not plus) volume to HFS+, which was useful back in the days that hard drives were actually expensive--I bought it, anyway, and it worked fine (back then converting to HFS+ on a decent-sized hard drive was like getting free space, due to the huge minimum block size of HFS).
That said, I'm not aware of any utility to convert from HFS+ to NTFS or FAT in a single step (apart from the multiple repartition mentioned above, which might work but sounds like it's asking for corruption), and given the tiny number of people who would want to do such a conversion--not to mention how cheap external hard drives are now--I'm skeptical that one does or will ever exist.
Microsoft rightly saw it as useful to be able to convert your boot drive from FAT to NTFS, because it's so hard to clone Windows; there's zero reason to convert a MacOS boot drive to NTFS, and if it's a data volume a backup and reformat to a brand new external would probably cost less than the software.
Question: Do you not really care about any of the data on that external? Because if you don't have a backup, you're essentially saying "I don't actually care about this data, since I will eventually lose it to bad luck." Common sense and any number of threads here will tell you that it's not a matter of if, but when a hard drive fails. Now, if it's your BitTorrent drive or something, then maybe you really don't care, in which case maybe the multiple-partition-resize scheme is what you want to try.
