Meadow will be the first team to face Scottish Premier League opposition since the introduction of Junior sides into the competition three years ago, and it is their reward for overcoming Selkirk and Second Division side Arbroath in previous rounds.
"I think we have done a lot of the work in the other rounds to show that we are a decent side," said Strain.
"This might be a step too far - Hibs are an exceptional side and they are third in the SPL at the moment.
"But we could hold our own in the lower leagues in Scotland no problem. We just need to relax, enjoy the occasion and play some good football."
Strain has been impressed by Hibs boss John Hughes and what he has achieved at the Edinburgh club so far this season, and admits his own usual tactics will have to change significantly this weekend in a bid to contain their hosts at Easter Road.
Strain said: "They have been fantastic, they are playing football the way it should be played and they have some really good players with plenty of experience.
"We will need to tighten up a little and it might not be the usual game we play. We are usually on the offensive and we will probably find that we are doing a lot of the chasing in this game."
The clash at Easter Road is one of the few fourth-round ties which looks set to go ahead this weekend, with weather conditions wreaking havoc with the fixture card.
Meadow trained at Rangers' Murray Park complex on Thursday night but Strain admits preparations for the biggest game in the club's history have been hit hard by the big freeze.
"The conditions have really hampered us," he said.
"We have been indoors a lot and went on the beach a couple of times so it really hasn't been ideal.
"We had a run-out on Tuesday against St Mirren and we were pretty rusty-looking as we hadn't played for a month but hopefully that has done us a power of good."
With fans able to pay at the gate, Strain hopes the number of travelling fans could swell to around 3,000 on the day.
He said: "There would have been absolutely no chance of it going ahead if it had been a home game. Our park is covered in snow and it's brick hard.
"But they've got the undersoil heating which has been left on so the game should be okay.
"All the lads are really looking forward to it and it would be a major disappointment if it was called off now."