Pinking shears will keep seam edges from fraying. You can prob find a zz attachment at ebay if that's what you'd rather have.

There a number of seam finishes you can use that do not involve zigzag stitching.You can find them in most sewing books. I've sewn on straight stitch machines all along & prefer to use those types of finishes, even tho I do have a serger - they are what you'll find on better quality garments. Try searching using the term "seam finishes"...

Here's a page w/ a few of them:

http://www.seasonedhomemaker.com/finish-seams-without-a-serger/

The most solid and best looking seams are often flat felled seams or frech seams. Especially finer light fabrics need the double stitching of the flat felled seam for strength and support. The Featerweight has two very nice feller feet, a narrow and a wide one. It can be ideal instead of a stretchy seam.

For finishing hems there are several ways about the zigzag or overlocker seams on most fabrics. The only thing you cannot get is a stretchy seam that maches the stretchiness of the fabric, but there are ways about even the stretchiest fabric when using only straight stitching.

If the fabric frays horribly you can cut out pieces with pinking shears then sew a straight seam along the edges, with a fairly short stitch and fine thread. you can even sew along the marks before you cut out the pieces. (Silk velvets for example can be difficult that way). With the worst fabrics you will probably need to tidy up a bit of loose threads along the edges even when using pinking shears.

Some of the zigzaggers for the old straight stitchers are easier to work with than others. The narrow types from Singer and Greist are nice, the ones with small flat cams or built in cams you regulate with a lever on the side. There are lots of different zigzag atachments, I have only tried the most common ones. The large black zigzagger with cams that look like red knobs is horrible to edge with, it stitches niced but it's very hard work to guide the fabric and get the seam in the right place.

True flat-felled seams can be a bit tricky, so I've often done a 'mock' flat-felled seam by stitching the seam, the pressing to 1 side & running 2 rows of 10-12/per inch topstitching on the outside of the item, 1 a hair away from the seam line & another 3/16" - 1/4" away, catching the seam allowance, using the presser foot as a guide. Excess fabric can be trimmed away from the seam allowance using pinking or straight shears, depending on fabric.

This can also be done w/ only 1 row of topstitching near the seam. It works best w/ straight seams.

FWIW, the only sewing machine I had for years was my mom's old featherweight - I made everything on it, & my current workhorse machine is an old Singer straight stitch as well.

I haven't seen zig-zag seam finishing for years. I do see a lot of serging.

You can buy zig-zag attachments for the featherweight. I have one and have had others through the years. Google "Singer...." and you will find them on eBay.