Could you call
ax2._get_lines.get_next_color()
to advance the color cycle by color. Unfortunately, this refers to a private attribute ._get_lines, so it is not part of the official public API and is not guaranteed to work in future versions of matplotlib.
A safer, but less direct way to develop the color cycle is to build a zero graph:
ax2.plot([], [])
import numpy as np
import matplotlib.pyplot as plt
x = np.arange(10)
y1 = np.random.randint(10, size=10)
y2 = np.random.randint(10, size=10)*100
fig, ax = plt.subplots()
ax.plot(x, y1, label='first')
ax2 = ax.twinx()
ax2._get_lines.get_next_color()
ax2.plot(x,y2, label='second')
handles1, labels1 = ax.get_legend_handles_labels()
handles2, labels2 = ax2.get_legend_handles_labels()
ax.legend(handles1+handles2, labels1+labels2, loc='best')
plt.show()

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