I would definitely recommend going and you will feel safe there as a woman traveling solo. This summer there were a couple of solo female travellers on the Hanoi to Luang Prabang flight. We would see solo travelers throughout our 5 days there. There are a lot of tour agencies on the main street. The prices are about the same I think. Luang Prabang is easy enough to walk to a couple of main attractions in the town itself. If you have ever been to Banff, Alberta in Canada, Luang Prabang reminded me of there, except in Laos and with a French Colonial influence.
Absolutely safe as a single female traveler, usual precautions as when traveling anywhere, but I feel a lot safer in SE Asia than I did living in Denver for 20 years. LP is a great town, and while two days will be short it will give you a taste and decide if you want to return. Spend a day just wandering through the town and the many wats, night market, a day trip to the waterfalls with a stop at the butterfly farm and you’ve filled two days. I’m looking forward to returning in December for a third visit.
You will be safer than you would be in the US.
No problem with safety in LP and if you stay in the center no need to take a tour as everything is within walking distance. You could join an early morning boat trip to Pak Ou caves where you will find 1000's of Buddha images that were only discovered not so many years ago.
It's rather sad that so many travellers from N.America feel the need to ask about 'safety'.
What Rufuscat says is absolutely right. I've been travelling around Asia for 13 years and met many solo female travellers. All happy, enjoying themselves and feeling 'safe'.
You'll enjoy Luang Prabang!Edited: 16 October 2018, 17:19
I felt it was pretty safe. We went to the Pak Ou Caves, night market, rode bikes to Phousi Hill, and witnessed monks receiving alms.
I wrote a trip report with our itinerary, photos, and some costs - might help you to get some ideas:
LP is such a relaxing town that you won't want to rush away - at least that's how I felt. There is plenty to occupy you in and around LP for two days.