Win 10 won't load from SSD without old HDD

by now i’ve read a number of topics with similar questions but the answers vary heavily from running a single line of code in CMD to multiple-page instructions on creating a Windows fix USB stick and doing some other seemingly sophisticated stuff, so it’s quite unclear as to what actually needs to be done in my particular situation, which is as follows:

• My 2nd PC had an HDD with Win 7 installed. As SSDs are cheaper than ever these days i decided to upgrade the performance on that machine.
• I purchased an SSD and installed Win 10 on it, however i did NOT
  unplug the old HDD during the install, which i now know was a
  mistake.
• Everything worked fine – on boot the PC asks if i want to load Win 7
  from the HDD or Win 10 from the SSD, both options worked (and still works if the SSD and HDD are both plugged in).
• Last week the HDD started making all sorts of noises hinting it will
  die sooner rather than later. As I had some documents and photos on that HDD which i still need i’ve bought a new SSD and have transfered (copy-pasted the folders i needed) the folders to this new SSD for storage (not the one with Win 10 installed)

And this is where things got tricky: i thought that all i had to do now was to simply unplug the old HDD and have my 2 SSDs plugged in for the system to work – one SSD where i had my Win 10 system installed, and new SSD with the folders copied from the old HDD for storage purposes.

But Win 10 won’t load without the old HDD plugged in. At first I thought there was an issue in the BIOS boot settings, but it’s not the case.

Having read up on the topic i can guesstimate that because i originally didn’t unplug the HDD during the Win 10 installation onto the SSD, Windows has automatically placed the boot data from both Win 7 and Win 10 onto the old HDD.

The question is:
Is it possible to “move”/”copy” the loader or create a new loader for the existing Win 10 system to the SSD, without reinstalling Win 10, and remove the HDD from the system all together? If yes, then what are the step-by-step instructions?

Details from Disk manger:
Screenshot of Disk manager HDD + SSD

• The HDD (Win 7) is marked as Disk 0 – 100 Mb reserved by system (attributes translated: System, Active, Main) – assume this is the loader; Disk “E” (Main) 195Gb; Disk “F” (Main) 270Gb – are two file partitions on the HDD;
• The SSD (Win 10) is markede as Disk 1 – “C” disk (attributes translated: Load, Paging file, Emergency memory dump, Main), 493Mb (back-up partition?)

If i “right-click” on the SSD “C” partition, the option to make it active is not greyed out

Details from diskpart:

Diskpartition HDD Partititon 1 (Boot partition?)

Diskpartition HDD Partititons 2 (Win 7) and 3

Diskpartition SSD Partititon 1 (Win 10)