Here is my take:
Jo Davidson could be related to a witness, criminal or a police officer. The fact that this DNA has been stored on other police databases does not mean that it cannot be a police officer, it may just mean an officer from another station.
My first thought was that Jo was related to Tommy Hunter, but it almost seems too obvious.
Here is a list of candidates and why it may or may not be them:
1. John Thomas Hunter
This seems to be the obvious choice. They are both Scottish, and it would explain Hasting's reaction. Tommy was born in the 60s and Jo was born in the 70s, so if they were related it would have most likely been in a brother-sister capacity. There is the potential for them to be father-daughter, but the explanation would be too complex and veer away from the main plot of the series.
** the explanation being that Tommy was raised in care and groomed by a female carer (Jo's mum), which resulted in Jo. The OCG found out this information before Jo did and used it to blackmail her. This explains her anger towards her mother. Her reluctance to take down the picture could be explained by the fact that she and her mum were close when Jo was growing up and she is still wrangling with disbelief.
2. John Corbett
I really can't see it being John Corbett. Corbett was born in Belfast. When his mother disappeared, he went to live with other family in Liverpool. If Jo was his sister, surely they would have been moved to Liverpool together? I also can't see a resemblance between the photos of Corbett's mum and Jo's mum, aside from having the same hairstyle.
3. Danny Waldron
I am not sure about this one. I mean... he was raised in a care home? She could be his sister. I don't know, it seems unlikely.
3. Dot Cottan
I am almost certain it isn't him. The phrase "other police database" makes me feel as if she is not related to an officer that works for (or in Dot's case, has previously worked for) AC-12.
4. Ted Hastings
The same explanation for Dot applies in the case of Ted. Plus, Ted would have been with Roisin at the time Jo was born and I cannot see Ted cheating on Roisin.
4. Terry Boyle
He is a candidate. Unlikely, but still a candidate. I feel as if Jo is too caring to be a long lost mother type.
5. Ryan Pilkington
It is not Ryan. We met Ryan's mother in S1 - she was young and disinterested. Arguably, she is to blame for Ryan's involvement in the OCG as she left her son to fend for himself on a dodgy estate.
6. Patrick Fairbank
I can't remember too much about pedalo Patrick, could it be him?
7. Mike Dryden
He was Scottish, too. Could he be her brother? Is he old enough to be her father?
8. Alastair Oldroyd
She didn't seem to react when he died. I don't think it's him. It also wouldn't garner the "Mother of God" reactions from Hastings, I don't think.
9. Carl Banks
Same as Alastair.
10. Derek Hilton
Unlikely. Too young to be her father.
11. Jeremy Cole
Maybe? Brother-sister?
12. Lester Hargreaves
Is he old enough to be her father?
13. Linus Murphy
Probably not.
14. Oliver Stephens-Lloyd
Probably not.
15. Robert Denmore
I can't even remember him. Probably not.
16. Rod Kennedy
Again, probably not.
17. Ronan Murphy
Probably not.
18. Tim Ifield
Probably not.
19. Nigel Morton
It would be cool. I just want to see Neil Morrissey again ahaha.
20. Philip Osborne
Maybe?
21. Michael Farmer
Unlikely, but we never saw his mother?
22. Nick Huntley
Probably not.
Another thing I've been thinking about...
If Jo's relative could be identified through a search of Farida's house, could Jo's have been identified if her relative's house was searched? This suggests that either somebody in the relative's investigation was covering this up, or her relative's house has never been searched in relation to a wider database (ruling out the likes of Michael Farmer).