Old shimx64.efi prevents update of UEFI.mdx

I am trying to update UEFI.mdx from 238 to 371.
But I have a couple of eufi entries that I think was left over from a previous Ubuntu install, from before I switched to Neon. Problem is, that one of them appear to be still active.

efibootmgr -v
BootCurrent: 0004
Timeout: 0 seconds
BootOrder: 0001,0004,0006,0008,0018,0019
Boot0000* Windows Boot Manager  HD(1,GPT,f887bce0-a023-4ee8-8b03-fef3047a9a24,0x800,0xfa000)/File(\EFI\Microsoft\Boot\bootmgfw.efi)WINDOWS.........x...B.C.D.O.B.J.E.C.T.=.{.9.d.e.a.8.6.2.c.-.5.c.d.d.-.4.e.7.0.-.a.c.c.1.-.f.3.2.b.3.4.4.d.4.7.9.5.}...n................
Boot0001* neon  HD(1,GPT,f887bce0-a023-4ee8-8b03-fef3047a9a24,0x800,0xfa000)/File(\EFI\neon\shimx64.efi)
Boot0002* Linux Firmware Updater        HD(1,GPT,f887bce0-a023-4ee8-8b03-fef3047a9a24,0x800,0xfa000)/File(\EFI\neon\fwupdx64.efi)
Boot0003  ubuntu        HD(1,GPT,f887bce0-a023-4ee8-8b03-fef3047a9a24,0x800,0xfa000)/File(\EFI\ubuntu\grubx64.efi)
Boot0004* Grub Menu     PciRoot(0x0)/Pci(0x1d,0x0)/Pci(0x0,0x0)/NVMe(0x1,64-79-A7-80-60-00-00-26)/HD(1,GPT,f887bce0-a023-4ee8-8b03-fef3047a9a24,0x800,0xfa000)/File(\EFI\ubuntu\shimx64.efi)
Boot0006* Diskette Drive        BBS(Floppy,Diskette Drive,0x0)..BO
Boot0008* CD/DVD/CD-RW Drive    BBS(CDROM,CD/DVD/CD-RW Drive,0x0)..BO
Boot0018* USB Storage Device    BBS(USB,USB Storage Device,0x0)..BO
Boot0019* M.2 PCIe SSD  BBS(HD,CT2000P3SSD8 ,0x0)..BO

I have windows 10, and two NEON installs in my system.
The efi entries I think is blocking the update are these:

ls -l ubuntu/
total 3404
-rwx------ 1 root root     108 Oct 19  2017 BOOTX64.CSV
-rwx------ 1 root root     117 Aug 31  2018 grub.cfg
-rwx------ 1 root root 1133944 Apr  4  2018 grubx64.efi
-rwx------ 1 root root 1168464 Oct 21  2017 mmx64.efi
-rwx------ 1 root root 1169992 Oct 21  2017 shimx64.efi

There are grubx64.efi and shimx64.efi in /boot/efi/EFI/Neon

ls -l Neon
total 4396
-rwx------ 1 root root     108 May  5 16:41 BOOTX64.CSV
drwx------ 2 root root    4096 Oct 20  2020 fw
-rwx------ 1 root root   60602 Jun 18  2020 fwupdx64.efi
-rwx------ 1 root root     117 May  5 16:41 grub.cfg
-rwx------ 1 root root 2598792 May  5 16:41 grubx64.efi
-rwx------ 1 root root  860824 May  5 16:41 mmx64.efi
-rwx------ 1 root root  960472 May  5 16:41 shimx64.efi

Is it safe to point the ubuntu efi entries to the files in Neon directory, and remove the ubuntu directory entirely? And if so, how do I update the efi entires?