A jeweler isn't a likely profession for the Viking Age. Dress adornments (erm, jewelry) came in a few different sorts. Most of what survives is metalwork, although I'd actually suggest thinking about beads rather than jewels. A quick review of clothing and adornment:

Men seem to have worn pretty simple clothes with a big pin holding a cloak at the neck and fancy belt buckle options, which suggests they might've had some decent leatherwork, too. Most metalwork was bronze or silver. You might find also find silver arm rings. Wealthy men might've shown off the quality of their textiles, and they took pride in how they groomed their hair and beards. Despite recent TV shows, there's no great evidence for tattoos.

Women wore flashier things. They had multiple layers, so again, there were opportunities to show off the quality of textiles. In their case, this probably meant a basic white linen shift, an apron sort of dress on top, and then a cloak wrapping around the shoulders. Women might wear brooches where the shoulder straps joined the front of their dresses, and sometimes they had another one or two for the cloak as well. These were typically bigger affairs, most often oval shells, so typically described as tortoise-shell brooches in the literature. The top margin of their dress between the brooches might be embroidered, or they might string beads between them. (You'll often find references to Viking-Age necklaces, but they seem to have been attached to the front of the dress—sometimes in multiple rows—rather than hung around the neck.)

Beads were pretty common, but they were also a way to show off. Children (boys and especially girls) might have a handful. Once girls reached an age for betrothal (early teens), fancy families would deck their daughters in massive necklaces, sometimes hundreds of beads. They'd often be pretty basic, maybe long strings of blue or silver-foil (check out the one on the left from Dublin; here's something similar from Norway), but they were numerous. Once women got older, their necklaces got smaller. Beginning around age 45 or so, the typically had very small necklaces of fewer than a dozen beads, although these beads were more likely to be larger, decorated beads instead of the plain numerous ones of their youth. (See the Dublin necklace on the right, which has a big amber bead in the middle.)

So instead of a jeweler, you might recast yourself as a bead maker and importer. Locally made beads tended to be bigger, though still just a centimeter or so, and decorated if they were fancy, or simple monochrome rings or barrels if they were basic. Some of these would go to children, and men might carry a pocketful (or perhaps attach them to their swords or sheathes?), but most would go to women. Almost all local beads were made from glass, with blue, red, white, and green being favorite colors. Sometimes you'd find amber beads, and these might be biggish balls or even pendants, sometimes shaped like a Thor's hammer. A few of the quartz beads might also be local, but quartz and certainly carnelian beads were more likely to be imported. These came from as far away as India. Here's a good example from Hedeby with two purple amethysts (pretty rare in the Viking Age) and a silver bead in the middle. Rock crystal (aka quartz) and carnelian necklaces were especially popular in the late 800s, when the historical Ragnar was bouncing around. You'd also find segmented beads of blue and silver- or gold-foil, again, like the Dublin necklace on the left.

At any rate, that's probably as close as you're going to get to gemstones. Some old garnets and things floated around among the elites, but these were probably gifted or kept as heirlooms and wouldn't pass through the hands of a jeweler. Glass, rock crystal, and carnelian would probably all be buffed with a basic cloth and not brought to a high shine. I can't say I've ever encountered a reference to sharkskin in the literature I've read. I'd have to look up what they worked amber with, but my first guess would be stone.

There was a lot of variety to the Viking Age, and what went on in the British Isles might have differed from things in various parts of Scandinavia or Iceland. Women often dangled things like knives and keys from chains, for example, and they might wear these differently in different places. Thor Ewing's book Viking Clothing is an obvious place to start, and there's a fair number of sites out there with varying degrees of reliability. Here's the National Museum of Denmark, and here's a pair of links that I've enjoyed looking through, and here's another pair of links from the Viking Answer Lady, who usually provides good resources.