When I first budded Yuzu, I collected older leafless wood, because the newest flush was too close to shooting and too thin. Similar to you, the sticks were rather flat.. The buds are there, above the thorn/petiole scar. I think a lot of the twiggy wood on Yuzu is similar. Maybe because it seems semi-deciduous. Just cut your buds as normal.
As Mr Texas says, sticks with well developed buds are better, probably because they are set to shoot, so will take off faster.
In many cases, you have to use the budwood you can get or are given. Not everyone appreciates you chopping up their plant for ideal budwood either, so sometimes you have to make do with what is available.
When you buds take, they may be slower to shoot than with other budwood?