I use alpine standard 3.8.1, which has kernel 4.14.82-0-vanilla.
When I start wireguard as client peer with wg-quick up client, It says:
 
[#] ip link add client type wireguard
[#] wg setconf client /dev/fd/63
[#] ip address add 10.0.0.4/24 dev client
[#] ip link set mtu 1420 dev client
[#] ip link set client up
[#] resolvconf -a client -m 0 -x
[#] wg set client fwmark 51820
[#] ip -4 route add 0.0.0.0/0 dev client table 51820
[#] ip -4 rule add not fwmark 51820 table 51820
[#] ip -4 rule add table main suppress_prefixlength 0
sysctl: unrecognized option: r
BusyBox v1.29.3 (2018-11-21 11:45:56 UTC) multi-call binary.

Usage: sysctl -p [-enq] [FILE...] / [-enqaw] [KEY[=VALUE]]...

Show/set kernel parameters

    -p    Set values from FILEs (default /etc/sysctl.conf)
    -e    Don't warn about unknown keys
    -n    Don't show key names
    -q      Quiet
    -a    Show all values
    -w    Set values
 
The client peer cannot ping server peer.