grafting and rooting offsets of Toumeya

I recently got a Toumeya papyracantha that is grafted to Trichocereus huascha that has produced several offsets on the sides. i plan to graft a few of these next spring and also try root one or two and grow them on their own roots. Will the removed offsets of this species produce roots? If not i obviously won't bother. anyone done this before? i really don't want to waste a single one.
I have read that self-rooted culture of Toumeya is difficult but possible, requiring cold dry wintering, careful watering and an extremely well drained soil mix.

Also i an unsure about which grafting stock to use for this plant. I want something that is strong but relatively slow growing and cold tolerant (no hylocereus!). Toumeya is from New Mexico and is of the most cold hardy cacti and can take -25C when dormant. I want the Toumeya scion to look natural on a short stock, not overly-inflated or distorted like on some trichocereus or hylocereus. preferably North American so it follows roughly the same growth pattern as the Toumeya as well. My specimen grafted on T.huascha is unnatural in size, although now i can use it as a stock plant for offsets and possibly seed as well. Is Toumeya self-fertile?
so..
Echinocereus sp.? dehydrates considerably in winter, cold hardy, following same growth pattern and not overly fast growing. but not often used as a stock and i don't know what species to use. i have seen Aztekium ritteri grafted to a soft spineless echinocereus sp. with surprising results. i got this idea because i heard that some of the difficult to cultivate Pediocacti and Sclerocacti, very close relatives of Toumeya, have been grafted to Echinocereus. sp. with excellent results.
or Myrtillocactus?..mexican so same growth pattern, not extremely fast growth. i have used it before, good growth rate, easy to come by, easy to work with.
Trichocereus pasacana? i have read that this is often used in Europe as a stock if slow growth is desired. but its huge, very spiny and not north american.
perhaps i will have to try as many stocks i can find and find the best one.

lewis wrote:

Will the removed offsets of this species produce roots? If not i obviously won't bother. anyone done this before? i really don't want to waste a single one.

Lewis I have noid but if you send and email to the seller. I am sure he will answer you

I got it at a CSSA meet. The seller i got it from did not grow the plants, rather was selling them for a friend to clear some bench space, i have no idea who the grower was, someone in Adelaide i think.
There were also some awesome grafted Echinomastus, Echinocereus, Sclerocactus and Pediocactus. All real North American rarities. I really wish i had known beforehand so i could have brought more money and got some more lol.

I have just been told an absolutley awesome idea of using Echinocereus viridiflorus as a stock, used in the US for Toumeya and its relatives.
It's perfect... relatively slow growth rate, same growth pattern, extremely hardy... cold tolerance -25C when dormant, North American, soft spines, serious winter dehydration (3/4 body weight) and small size means that a short stock can be used and easily concealed with top dressing so the Toumeya scion looks like an own-rooted specimen.
And best of all i already have it in my collection!! worth growing on its own merits for the remarkable green flowers with a strong lemon-scent. Mine are coming into bud now.
Time to get propagating and buying more E.viridiflorus i'm thinking