Warriors forward Mefin Davies will replace McBryde, with 34-year-old veteran Gareth Llewellyn winning his 84th cap as deputy for Sidoli.
"If it had been a game to secure the Grand Slam, then maybe both Sidoli and McBryde could have played," said Hansen.
"But we have taken a long-term approach with both of them. They should be back in contention for the Ireland game (on Sunday week), but for the time being we are happy with the make-up of the team."
Hansen has made eight changes, including two positional switches, from the team beaten 28-17 by World Cup quarter-final opponents England in Brisbane three months ago.
Prop Duncan Jones and centre Sonny Parker return to the side after being unavailable because of injury, while Rhys Williams replaces injured wing Mark Jones and flanker Martyn Williams is recalled instead of star World Cup performer Jonathan Thomas.
The positional alterations are both in the back-row, where skipper Colin Charvis reverts to blindside flanker and Dafydd Jones features at number eight.
Substitute hookers Gareth Williams and Huw Bennett are bracketed together on the bench, with Williams facing a fitness test.
Gareth Thomas will play his first game at full-back for Wales on home soil. He moved there with great success during the World Cup campaign.
Wales team to play Scotland in the RBS 6 Nations Championship at the Millennium Stadium on Saturday:
G Thomas (Celtic Warriors); R Williams (Cardiff Blues), S Parker (Warriors), I Harris (Blues), S Williams (Neath-Swansea Ospreys); S Jones (Llanelli Scarlets), G Cooper (Warriors); Duncan Jones (Ospreys), M Davies (Warriors), A Jones (Ospreys), B Cockbain (Warriors), G Llewellyn (Ospreys), C Charvis (Tarbes, capt), M Williams (Blues), Dafydd Jones (Scarlets).
Replacements: H Bennett (Ospreys) or G Williams (Blues), G Jenkins (Warriors), M Owen (Gwent Dragons), J Thomas (Ospreys), D Peel (Scarlets), C Sweeney (Warriors), T Shanklin (Blues).