Right, well, according to the version of the Redemption rules I have (which as far as I'm aware are the most up-to-date ones), weapons used by Priests and Deacons are listed under the "Priesthood" weapons, and the one of interest to us is "Priesthood Special Weapons".
As these are the Redemption's own versions of special weapons, and noted as such, the Techno rule almost definitely qualifies here. An example of something you could not get through the Techno skills is Zealot equipment, as these are basically considered to be "Unique" equipment (as per the FAQ, I can find the page if necessary) and thus are only available to those who are permitted to use it. Not even gangs that capture this equipment could use an Eviscerator, unless they also had a Zealot, which is unlikely.
It appears my version of the Redemption rules also contains a note which says thus:
Note: If a member of your gang gets the Specialist skill he would gain access to the Priest Basic and Special Weapon Lists
As to other equipment from trade charts, they are restricted to weapons only on their weapon lists, and the restrictions on those lists applies to any weapons bought on the trade chart. Some weapons cannot be bought, but these are things like Plasma Guns, that aren't on the weapon list. Equipment however, is not subject to this restriction. As per the Redemption rules:
Redemptionists gangs can only buy additional equipment from the Redemptionist weapon lists and may not acquire or use weapons which are not on this list.
(emphasis added)
As the passage specifically refers to weapons, equipment are exempt from this ruling. So yes, you can take any non-weapon equipment from the trade chart that you can afford. The "One in a Million Weapon" is mentioned, and is equipment, technically, but it also requires the purchase of a weapon type, and it is this specific aspect that the restrictions placed in the Redemption rules are referring to. Normally Techno allows additional access to weapons on trade lists, but the Redemption rules specifically cater against this.
For prosperity other Outlander players may find this particular FAQ entry of interest:
Q: Can I use the Marksman Skill with my lasgun in a Ratskin Gang, can I ever get a plasmagun?
A: Ok, this is a tough one. When your gang rules put a weapon is in a category other then what the weapon is listed
in the ORB Armoury Section it stay the same in the ORB Armoury Section for skills and equipment use. Also, if a
fighter gets the Specialist Skill he will be able to use any Special Weapon in the ORB Armoury Section. In this case, if
your gang rules have other or different Special Weapons then you may also use those since 99% of the time those
weapons are ORB Armoury Section Basic Weapons anyway. [Answer Mod FAQ p.42]
This at least will explain why the specialist skill also allows the use of some basic weapons. Remember that the restrictions imposed upon the Redemption rules overrule the scope of the Specialist Skill, but you can use special and basic weapons available to Deacons and Priests as you requested.
Hope this helps.