Yes, you can absolutely trek to Tapovan without any travel guide. Gaumukh Tapovan trek is one of the most beautiful trek in India which takes you to the origin of Bhagirathi and beyond. The trek starts from Gangotri. If you want to trek upto Tapvan , you will need a pass from forest department. You can get the pass at Uttarkashi; however, if you wish, you can also get this pass at Gangotri as well. The office will be open from 10-12 in the morning and 2-4 in the afternoon. The officers will ask for your identity proof and how you are trekking. Now, if you want to trek without any travel guide, I suggest you to visit this office of forest department, you will be able to find plenty of solo trekker over there and some groups as well. Join any of them and you are good to go.You can stay at Lalbaba ashram in Bojwasa for the first night or camp at Chirwasa. Since the trek is really tricky after after Gaumukh glacier, I would suggest you to please find a group or other solo traveller in Gangotri which is really easy. I trekked to Tapovan last year and found a couple at Gangotri. I would suggest you to take atleast five layers of clothing because the wind on this trek is very strong and chilly. I hope you got your answer. Happy and safe trekking.