After 20+ years of DYI ponds, I agree that you are probably better off with a new thicker liner. From experience, cutting corners will result in bigger problems in the near future.

To add to the advice above, get liner that can fully cover the concrete and use the old liner as an under layer (dont throw it out!). I have done this and use Silicone foam and/or sealant to connect the liner to concrete (after cleaning and drying it fully). I use these products.

Aquascape Black Silicone Sealant, Safe for Fish, 10.1-ounce |29186 https://smile.amazon.com/dp/B000N1AMY0/ref=cm_sw_r_cp_api_i_A2WFS5393NEDG5NCBVWD

Dap 40440 12 oz. Touch 'n Foam... https://www.amazon.com/dp/B000BQWLCS?ref=ppx_pop_mob_ap_share

To hide the liner, I have access to almost unlimited bricks and pavers and use these around the edges to hide the liner. Slates or other flat rocks also work for this purpose. Here is a photo of a repair I recently did following this technique: https://imgur.com/a/j8w5wtm