The AFC Bournemouth youngster has spent time on loan in non-league and at Burton Albion - and was wanted by a host of clubs leading up to the end of the window.
The Montgomery Waters Meadow was Saydee’s destination of choice - and he revealed how conversations with Cotterill and the impact he had on Udoh’s Salop career were the two selling points.
Udoh bagged 15 goals in all competitions last season - his first full campaign under Cotterill.
“It was about choosing the right team,” explained Saydee.
“When I spoke to the gaffer, the way he painted the picture for me I thought, yeah, Shrewsbury is the club for me.
“I had quite a few options but after speaking to the gaffer, he was strong on me coming here, so I listened to him and decided to come here.
“It was how he is, and how he pushes players.
“With Dan, Dan didn’t score many goals and then the gaffer comes here and he scores more.
“As a striker, you look at those things and maybe you he can do that for me.
“I really like him. He has really pushed me since I have been here and I feel like I’m going to become a better player under him.
“Training is tough but it’s to make me better so I am enjoying it.”
The striker has turned out five times for the Cherries and netted once since joining the club’s academy from Reading.
And prior to joining Salop, he was sent on loan spells to Poole Town and Weymouth, before spending half of last season with Saturday’s opponents, Burton Abion.
He was handed his first start at Port Vale last week and repaid Cotterill’s faith by netting Salop’s goal in the first period.
The striker explained how he has settled in well to life at the club and now wants to kick on and become the main striker this season.
He said: “It’s been good, I’ve got all with everyone. The boys have really helped me settle in and I’m enjoying it.
“The lads have been so good. It’s the same with Streety (Rob Street) and Wini (Carl Winchester). We have all gelled really well.
“I’m enjoying it so much.
“It was a really good feeling, to come here and score straight away – I was buzzing.
“As a striker, that type of thing can play on your mind. You want to score goals because that is what you are supposed to do.
“So for that first one to come, I’m very happy.
“I want to be the main starter, starting all the time, but there are other strikers and we want to drive each other and we’re all competing for that spot which is good.”
Saydee earned praise from former Cherries boss Scott Parker last month, for his display in the Carabao Cup penalty shootout win over Norwich City.
The AFC Bournemouth loanee started up front in the game - and Parker hailed his performance as magnificent.
Asked about his future goals back at the Cherries, Saydee added: “I have not thought about that, I just want to concentrate on getting as many goals as I can.
“I don’t want to think about the other side of it - if I score here then everything will fall into place.”