Hi,
I just finished my solo trip's vietnam leg and I'd say it is a pretty safe place for both genders given you travel a bit responsibly.
Here are a few things not to do -
Staying at a really cheap hotel or hostel - definitely not safe for your belongings.
Hop on any bike taxi or cab you see - use grab, its cheaper than most other options and safer too.
Jumping on a bike just coz the rider has a grab tshirt or jacket on - a lot of bike taxi drivers wear grab jackets or helmets but they are not grab taxis. So always book via grab or ask the driver to give grab code. If they are fake ones, they wont give code and you should move on. There are a lot of grab bike taxis so don't worry about losing the ride.
Not using lockers - Lock your stuff properly no matter where you are staying.
Expecting Free towels - Carry your own towel if you are staying at a hostel.
Booking cheap but far - Traffic is a pain in the ass in most cities. Book a hostel or hotel near the attractions you want to visit. For example, old quarter in hanoi or District 1 in Saigon. Most tours also use these locations as pickup points.
Booking tours from hostel - Never book a tour from your hostel or hotel. They charge way too much sometimes 3x more.
Expecting fast public transport- Public transport is very good for travelling from and to the airports. Dont book hotel taxis coz they get commission from the taxi drivers for bookings and they take just about 15-20 minutes more. But, it takes a lot more time in the old buses. Airport transfer buses are good.
Dont fall for tourist trap locations - you shouldn't have to visit a museum if you aren't interested. There are a lot more better things to do in Vietnam. Museums and such attractions are time consuming and drain a lot of money.
Spending on some fancy tours - Most tours are money traps. E.g., Dont spend more than VND 300.000 if you're going to cu chi tunnels in Saigon. Anything more than that means you are being ripped off.
Vietnam is pricey - And finally, $1 = ~VND 23.000 right now. Everyone ignores the .000 in Vietnam. They just say 20 or 30 and not twenty thousand. A mug of beer costs VND 5.000. Pretty fucking cheap I'd say.

Have a great trip!