If you didn't get a notice in webmaster tools about "unnatural backlinks", I wouldn't suggest disavowing any links. If you have a problem with too many exact anchors, its far better just to balance them out with more links of nonexact anchors.
As far as how to redirect it ... does it still get traffic? If so ... set the whole site up as a canonical to your new site. This transfers rankings quickly from one domain to another. 301 would also transfer the links that you say you don't want.
The reason I hate to disavow links is that, while Google can somewhat alleviate the penalty caused by it ... that penalty seems to snap back pretty easy. Far better just to balance the links out.
I hate most widgets just because they seem to elevate keyword density throughout the site. Be careful of the keywords they happen to inject on every page ... it makes it harder to use those same keywords in content without hitting the limit on density.
You're best off if you can use your own anchors on all the links and tone down repetition of your site's primary keywords.
Almost every update that resulted in bad rankings for someone was primarily a strict keyword stuffing filter which just got a little more strict. 150 words isn't very much content ... you can rank with low content + lots of links but its hard to rank on just low content. I'd recommend taking like 5 of those, improving them by bringing them back up to 300 or more words, and keep adjusting it like that until they rank.
Sometimes, I don't even know what Google is looking for ... if usually I can get a page to rank following the guidelines I listed, but worst case scenario I will just tinker by adjusting keyword densities, adding content ... keep doing that until the page ranks.
On a 5/6 word keyword its easy to stuff. You'll want to use the keyword once, and you will have to write a longer article. Use portions of the long keyword as well (break it down into chunks) and keep those chunks at their appropriate keyword densities as well.
For this ...
"how to make lightweight bike parts"
I would have this in title, and as such my template will also make it a H1 tag. I will use it in content at 1% or less. Because it is a 6 word keyword, that means you have to write more than 600 words minimum to get 1% density on this one keyword.
I'll break it up ... "If you're wondering how to make a bike that blah blah", (just used "how to make" again) ... I'd do that to 1% density on its own, seeing its a 3 word combo.
"Lightweight bike parts are important if you are building a bike that will blah blah" ... just used "lightweight bike parts" as another keyword on the page. Because its 3 word combo, I'd use that at 1% or less.
I'd use "how to" at up to 1.5% density, lightweight up to 2% density, "bike parts" at up to 1.5% density, bike and parts separately at 2%.
1.6% density is bordering overoptimization on a 2 word keyword ... I'd keep it lower.