Hi RMaxa
If you are using a standard dovetail jig you will need to used a dovetail bit
You can't get away without using it , On some jigs you can use a straight bit on one side but you must use a dovetail on the other side.
Give this a try, it works for me, take some double sided carpet tape and stick on some 1/8" or 1/4" MDF stock on both sides of the plywood, it only needs to be as wide as the dovetails or just a bit longer, then clamp it in the jig and put in the dovetails, you will still get just a little rip out but the MDF will at as a chip breaker and help hold the plywood from pulling out.
NOTE**** don't forget to add a 1/8" or 1/4" to your setting on the jig to off set the MDF stock.
Note**** if you are using blind dovetails you only need the MDF on one side (inside of the box cut) if you are making the side(s) and the front/back at the same time in the jig) this way you don't need to change your jig setting but the MDF must be the same size as "wide) as the box/drawer , but go slow on the ends and made very small cuts, out side 1st then move in.
You will also need to drop the bit down by 1/8" or 1/4" so the joint will fit right.
Hope this helps
Bj