Assuming there are typos in the examples given in the question.
My answer uses no decimals and no exponentiation.
Only two of the solutions use division.
Only two of the solutions use multiple-digit numbers.
Only $74$ and $77$ need multiple digits.
Only $83$ and $85$ need division.
$ 1 = 4 + 6 - 8 - 1 $
$ 2 = \sqrt{4} \times (6 - 1) - 8 $
$ 3 = 1 + 4 - (8 - 6) $
$ 4 = (4 - 1)! - (8 - 6) $
$ 5 = 8 - 6 + 4 - 1 $
$ 6 = (8 - 6) \times (4 - 1) $
$ 7 = 8 - 6 + 1 + 4 $
$ 8 = (4 - 1)! + 8 - 6 $
$ 9 = 6 - 4 + 8 - 1 $
$ 10 = (4 - 1) \times 6 - 8 $
$ 11 = 6 - 4 + 1 + 8 $
$ 12 = (8 - 6 + 1) \times 4 $
$ 13 = \sqrt{(1 + 8)} + 4 + 6 $
$ 14 = (6 - 4) \times (8 - 1) $
$ 15 = 4 \times 6 - (1 + 8) $
$ 16 = (6 - 1) \times 8 - 4! $
$ 17 = 4 - 1 + 6 + 8 $
$ 18 = (4 - 1) \times 8 - 6 $
$ 19 = 1 + 4 + 6 + 8 $
$ 20 = (1 + 6) \times 4 - 8 $
$ 21 = 4!! - 1 + 6 + 8 $
$ 22 = (8 - 1) \times 4 - 6 $
$ 23 = (8 - 4) \times 6 - 1 $
$ 24 = (6 - 4 + 1) \times 8 $
$ 25 = 4 \times 8 - (1 + 6) $
$ 26 = (4 - 1) \times 6 + 8 $
$ 27 = 4 \times 8 - (6 - 1) $
$ 28 = (6 - 1) \times 4 + 8 $
$ 29 = (1 + 4)!! + 6 + 8 $
$ 30 = (8 - 4 + 1) \times 6 $
$ 31 = 8 - 1 + 4 \times 6 $
$ 32 = (6 - 1) \times 8 - 4!! $
$ 33 = 1 + 8 + 4 \times 6 $
$ 34 = (8 - 1) \times 4 + 6 $
$ 35 = 6!! - (4 + 8) - 1 $
$ 36 = (1 + 6) \times 4 + 8 $
$ 37 = 6 - 1 + 4 \times 8 $
$ 38 = (1 + 4) \times 6 + 8 $
$ 39 = 1 + 6 + 4 \times 8 $
$ 40 = (1 + 6 - \sqrt{4}) \times 8 $
$ 41 = 6 \times 8 - 4!! + 1 $
$ 42 = (1 + 8) \times 4 + 6 $
$ 43 = 6 \times 8 - (1 + 4) $
$ 44 = (6 - 1) \times 8 + 4 $
$ 45 = 6 \times 8 - (4 - 1) $
$ 46 = (1 + 4) \times 8 + 6 $
$ 47 = (6 - 1)!! + 4 \times 8 $
$ 48 = (6 - 4 + 1)! \times 8 $
$ 49 = 6 \times 8 - 1 + \sqrt{4} $
$ 50 = (1 + 8) \times 6 - 4 $
$ 51 = 4 - 1 + 6 \times 8 $
$ 52 = (6 - 1 + 8) \times 4 $
$ 53 = 1 + 4 + 6 \times 8 $
$ 54 = (4 - 1)! + 6 \times 8 $
$ 55 = (6 + 8) \times 4 - 1 $
$ 56 = (\sqrt{4} + 6 - 1) \times 8 $
$ 57 = (6 + 8) \times 4 + 1 $
$ 58 = (1 + 8) \times 6 + 4 $
$ 59 = 4 - 1 + 8 + 6!! $
$ 60 = (1 + 6) \times 8 + 4 $
$ 61 = 1 + 4 + 8 + 6!! $
$ 62 = (1 + 8) \times 6 + 4!! $
$ 63 = (1 + 4)!! + 6 \times 8 $
$ 64 = (6 - 1) \times 8 + 4! $
$ 65 = (\sqrt{4} + 6) \times 8 + 1 $
$ 66 = (4 - 1 + 8) \times 6 $
$ 67 = \sqrt{(8!! - 4! + 1)} + 6!! $
$ 68 = (6 - 1)!! \times 4 + 8 $
$ 69 = 4!! \times 8 + 6 - 1 $
$ 70 = (1 + 4) \times (6 + 8) $
$ 71 = (4 + 8) \times 6 - 1 $
$ 72 = (4 - 1 + 6) \times 8 $
$ 73 = (4 + 8) \times 6 + 1 $
$ 74 = (4 - 1)! + 68 $
$ 75 = (8 - 1)!! - (4! + 6) $
$ 76 = (8 - 1) \times 4 + 6!! $
$ 77 = \sqrt{841} + 6!! $
$ 78 = (1 + 4 + 8) \times 6 $
$ 79 = (4 + 6) \times 8 - 1 $
$ 80 = \sqrt{4} \times (6 - 1) \times 8 $
$ 81 = (4 + 6) \times 8 + 1 $
$ 82 = (1 + 4)!! \times 6 - 8 $
$ 83 = \frac{6!}{8} - (4!! - 1) $
$ 84 = (1 + 6) \times (4 + 8) $
$ 85 = \frac{6!}{8} - (1 + 4) $
$ 86 = (6!! - 1) \times \sqrt{4} - 8 $
$ 87 = \sqrt{4} \times 6!! - (1 + 8) $
$ 88 = (1 + 4 + 6) \times 8 $
$ 89 = \sqrt{4} \times 6!! - (8 - 1) $
$ 90 = (1 + 8) \times (4 + 6) $
$ 91 = (8 - 1)!! - (4!! + 6) $
$ 92 = ((6 - 1)!! + 8) \times 4 $
$ 93 = (1 + 6)!! - (4 + 8) $
$ 94 = (6 \times 8 - 1) \times \sqrt{4} $
$ 95 = \sqrt{4} \times 6 \times 8 - 1 $
$ 96 = ((4 - 1)! + 6) \times 8 $
$ 97 = \sqrt{4} \times 6 \times 8 + 1 $
$ 98 = (1 + 4)!! \times 6 + 8 $
$ 99 = (1 + 6)!! - 8 + \sqrt{4} $
$ 100 = ((\sqrt{(1 + 8)})!)!! + 6!! + 4 $