I think that the Cautery/Remedy Signet combination is a good one, and is okay for condition renewal. However, Martyr has only a 10 second cooldown, making it available more often for you. Dropping Resilient Was Xixo can actually gain energy for you throughout the whole process of condition removal (depending on what weapons you have equipped). However, the 8 skills that you have listed are certainly viable for everyday play. I like the Rt/P combo, there are a lot of nice skills that Ritualists can utilize.
Now that I'm lookin' at your build some more, I must ask you - Where're your Weapon Spells? The Mighty was Vorizun/Soothing Memories combination is nice for energy management. I my very personal opinion, though, Restoration isn't worth the 25 Energy. Now, you could add in Life, as was suggested, but I might say to add in Vital Weapon, and swap Spirit Light for Wielder's Boon. This'll give you a comparable heal with the addition of the tank (or person who's taking damage) having 150 more HP to burn through. I'd also swap out Mend Body and Soul for Resilient Weapon, to "buy time" for your Cautery/Remedy skills.
So, because I fail at the internet, here are my non-sweet-link-build-ideas.
Vital Weapon - (more health for the tanks, lasts for 30 seconds)
Resilient Weapon - (to buy time for Cautery Signet, don't overuse)
Wielder's Boon - (solid heals on weapon-spelled people)
Soothing Memories - (to heal folks with no weapon spells on 'em)
Mighty was Vorizun - (Energy Management)
Cautery Signet - (you know why)
Remedy Signet - (you know why)
Flesh of My Flesh - (because the above 7 skills might not always work

)
The removal of Recuperation or any other spirit makes you much more mobile on the battlefield, because you never need to wait for cooldowns on those things. Weapon spells similarly cannot be removed, but spirits can be killed, meaning that not only do you lose the benefit of it, but you ALSO might not want to use Spirit Light or any other spirit-based spell either.
So yeah. I love Weapon Spells, basically.

But good idea with the Cautery/Remedy Signets! I might try that myself. Your original build should work perfectly fine, though, I'm just giving you my opinions and other options here.
Welcome to the Ritualist world!